Support is a Math Education Blog that aims to provide useful Math / Education content that helps people worldwide.

Over the years, has grown to reach 500,000 total views, thanks to support of fans!

If you find our website useful, please consider supporting it in one of the following ways. Thanks!

1) Link back to our page (

Every hyperlink counts! It could be a reblog, tweet, facebook, or a link in your blog. It doesn’t cost a cent, yet it is extremely important to the growth of the website.

2) Patreon

Our patreon page is at:

3) Buy yourself a gift at Amazon

Purchase any item at Amazon using this link: Amazon.

4) Buy a Math Resource

Our sales page is here:

5) Advertise on our website

Our advertisement page is here:

Thank you once again for your support.

Posted in math | Tagged , | Leave a comment

Math Blog

Subscribe to our free newsletter, for updates on Math, Education and other General Knowledge topics!

Enter your email address to follow this blog and receive notifications of new posts by email.

Posted in math knowledge | Tagged , | 1 Comment

Install Windows on MacBook (Fast and Easy method)

Basically, you just need to follow the instructions in the YouTube video below. It is very easy and fast. The key software is VirtualBox.

You can download the official Windows 10 ISO disc image here:

Note that Windows 10 (Home) is free (you don’t have to activate it) and you can use it with only very minor restrictions.

Overall, the process to install Windows 10 on a Mac (using VirtualBox) is much easier than I expected.

Total time taken: Around 30-40 minutes (possibly faster if your download speed and RAM is fast)

Total cost: $0

Total space needed: Around 10-20 GB is needed initially. VirtualBox allows “dynamically allocated disks” which are faster to create and can grow to larger sizes. For example, if you set 50GB as your disk space (but only use 10 GB) then it will only occupy 10 GB on your Mac.

Posted in Uncategorized | Tagged , , , , | 1 Comment

Aquatic Plants 水生植物

An introduction to the aquatic plants in my low tech tank:

1) AR Mini 迷你血心兰

2) Java Fern 铁皇冠

3) Dwarf Sag 矮慈姑

4) Cryptocoryne Wendtii 绿温蒂椒草

5) Giant Salvinia 槐叶萍

6) Anubias 水榕

7) Marimo Moss Ball 海藻球

Posted in Uncategorized | Tagged , , , , | Leave a comment

How to keep Python / R Running on Mac (without screen lock or sleep)

When the Mac (or MacBook) is running for a long time, it is very liable to do one of the following things:

  • sleep
  • screen saver
  • lock screen

The problem is that your Python program or R program running in the background will most likely stop completely. Sure, it can resume when you activate the Mac again, but that is not what most people want! For one, it may impact the accurate calculation of elapsed time of your Python code.

Changing settings via System Preferences -> Energy Saver is a possible solution, but it is troublesome and problematic:

  • Have to switch it on and off again when not in use (many steps).
  • Preventing sleep may still run into screen saver, screen lock, etc.
  • Vice versa, preventing screen lock may still run into Mac sleeping, etc.

The solution is to install this free App called Amphetamine. Despite its “drug” name, it is a totally legitimate program that has high reviews everywhere. What this app does is to prevent your Mac from stopping, locking or sleeping. Hence, whatever program you are running will not halt till the program is done (or when you switch off Amphetamine).

It is a great program that does its job well! Highly recommended for anyone doing programming, video editing or downloading large files on Mac.

Posted in Uncategorized | Tagged , , , | 1 Comment

Best way to time algorithms in Python

There are tons of ways to calculate elapsed time (in seconds) for Python code. But which is the best way?

So far, I find that the “timeit” method seems to give good results, and is easy to implement. Source:

Use timeit.default_timer instead of timeit.timeit. The former provides the best clock available on your platform and version of Python automatically:

from timeit import default_timer as timer

start = timer()
# ...
end = timer()
print(end - start) # Time in seconds, e.g. 5.38091952400282

This is the answer by the user “jfs” on Stack Overflow.

Benefits of the above method include:

  • Using timeit will produce far more accurate results since it will automatically account for things like garbage collection and OS differences (comment by user “lkgarrison”)

Please comment below if you know other ways of measuring elapsed time on Python!

Other methods include:

  • time.clock()  (Deprecated as of Python 3.3)
  • time.time() (Is this a good method?)
  • time.perf_counter() for system-wide timing,
  • or time.process_time() for process-wide timing


Posted in Uncategorized | Tagged , | 2 Comments

The Enigma of the Erasers (Homeschool Math Challenging Puzzles)

Dan has 745 red, green, blue and yellow erasers.

If the number of red erasers is tripled, the number of green erasers is halved, the number of blue erasers is decreased by 39, and the number of yellow erasers is increased by 48, there will be an equal number of erasers for each of the colors.

How many erasers are there for each of the colors?

This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:

  • Homeschooling for gifted kids
  • Preparation for GEP (Gifted Education Programme) screening and selection tests
  • Preparation for Math Olympiad
  • Puzzles for kids interested in math but find school work too easy.


Let the number of red erasers be 1 unit:

R -> 1u

3R -> 3u

This means that the number of green erasers must be 3u x 2 = 6u.

G -> 6u

(This is so that after the green erasers are halved, it is also 3u.)

B -> 3u+39

Y -> 3u-48


R+G+B+Y = 13u – 9 = 745

13u = 754

1u = 754/13 = 58.

Hence, the number of erasers for each color are:

R = 1u = 58

G = 6u = 348

B = 3u+39 = 213

Y = 3u-48 = 126

Posted in Homeschool Math Challenging Puzzles | Tagged | 1 Comment

Buy Prescription Glasses, Spectacles & Sunglasses Online from the UK’s Favourite Online Optician!

Online Opticians UK sell cheap prescription glasses & spectacles from just £14.95, designer glasses from £39.95, prescription sunglasses from only £39.95, glasses reglazing from £19.95 & varifocal glasses from just £49.95.

All of our prescription glasses include free anti reflection/scratch proof/UV coated lenses, worth £25.00, a stylish hard case and a microfibre cloth as standard.

All purchases are backed up by our 30 day ‘No Risk – No Quibble’ money back guarantee.

Posted in Uncategorized | Leave a comment

Worry Doesn’t Solve Anything

Source: Pastor Rick Warren


“Do not worry about your life, what you will eat or drink; or about your body, what you will wear. Is not life more than food, and the body more than clothes?”

Matthew 6:25 (NIV)

Worry is essentially a control issue. It’s trying to control the uncontrollable. We can’t control the economy, so we worry about the economy. We can’t control our children, so we worry about our children. We can’t control the future, so we worry about the future.But worry never solves anything! It’s stewing without doing.

Jesus actually gives four reasons you don’t need to worry in his Sermon on the Mount.

1. Worry is unreasonable.
Matthew 6:25 says, “Do not worry about your life, what you will eat or drink; or about your body, what you will wear. Is not life more than food, and the body more than clothes?” (NIV).

Jesus is saying, if it’s not going to last, don’t worry about it. To worry about something you can change is foolish. To worry about something you can’t change is useless. Either way, it’s unreasonable to worry.

2. Worry is unnatural.
Jesus gives us an illustration from nature in Matthew 6:26: “Look at the birds of the air; they do not sow or reap or store away in barns, and yet your heavenly Father feeds them. Are you not much more valuable than they?” (NIV).

There’s only one thing in all of God’s creation that worries: human beings. We’re the only things God has created that don’t trust him, and God says this is unnatural.

3. Worry is unhelpful.
It doesn’t change anything. Matthew 6:27 says, “Can any one of you by worrying add a single hour to your life?” (NIV). When you worry about a problem, it doesn’t bring you one inch closer to the solution. It’s like sitting in a rocking chair—a lot of activity, energy, and motion, but no progress. Worry doesn’t change anything except you. It makes you miserable!

4. Worry is unnecessary.
Matthew 6:30 says, “If that is how God clothes the grass of the field, which is here today and tomorrow is thrown into the fire, will he not much more clothe you—you of little faith?” (NIV). If you trust in God, you don’t need to worry. Why? Because he has promised to take care of all your needs: “God will meet all your needs according to the riches of his glory in Christ Jesus” (Philippians 4:19 NIV).

That includes your bills, relational conflicts, dreams, goals, ambitions, and health issues you don’t know what to do with. God will meet all your needs in Christ.

Don’t worry about it!

Posted in Uncategorized | Tagged , , , | Leave a comment

Seachem Root Tabs Review

Just added 1 Seachem Flourish Tab next to my Alternanthera Reineckii Mini (AR Mini). Some “fizzing” or bubbling is observed. Not sure if that is due to the root tab, or maybe I disturbed some gas pockets in the substrate.

I am still continuing the growing of AR Mini in low tech tank (see Alternanthera Reineckii Mini Low Tech).

Seachem Flourish Tabs Growth Supplement – Aquatic Plant Stimulant 10 ct

My dog Charlie curious about the Seachem Root Tab.

Seachem Root Tab Review

The below review video is rather convincing proof that Seachem Flourish tabs are one of the best root tabs in the market, despite having low macro nutrients (nitrogen and phosphate). The purpose of having low macro nutrients is for preventing algae.

Posted in Uncategorized | Tagged , , , | Leave a comment

Singapore PM Lee Hsien Loong Mentions Tropical Fish Shop in his speech on COVID-19

PM Lee Hsien Loong on the COVID-19 pandemic: “I am in this for a very long time to come. To sustain this, I need everybody’s cooperation – safe distancing, personal hygiene, cooperation when we are contact tracing and discipline when people come back, stay home notification, stay home.” (Video: PMO)


Something interesting in this speech is that PM Lee mentions the plight of a tropical fish shop owner in Singapore.

Time around 5.22:

PM Lee chats with a Tropical Fish shop owner in Teck Ghee, who has been there for “donkey’s years”. She says her supplies come from Malaysia, and Malaysia has locked down. Tropical fish is not an essential item, how does she get her business going?




Posted in Uncategorized | Tagged , , , | Leave a comment

Underwater Garden

Very low tech 5 gallon tank for my Phoenix Rasboras (Boraras Merah) and Neon Tetras. I just let the plants grow naturally without CO2, with occasional trimmings. If you look carefully, you can see the Horned Nerite Snail eggs (they look like sesame seeds)!

Posted in Uncategorized | Tagged , , , | 1 Comment

Home Cooked Food for My Dog Charlie

Cooking For Fun

My husband and I got this poodle Charlie last month. Ever since this little cutie came to our house, our life completely changed.

I feel so lucky to have such a little playful buddy as our family member.

Most time, Charlie has dog food which was bought from pet store. But sometimes, especially on some big occasion, I will cook for him.

Actually, cooking for dog is much easier than cooking for human, as there is no need to season or to make different flavor. Home cooked dog food has a very simple rule – boil.

Ingredients I use are always chicken breast, potato and carrot. Charlie is only 3 kg now. He was 1.5 kg when he first came. So Charlie has very little appetite. He can’t eat too much.

The very simple way to deal with ingredients is to chop everything into small dices. You can choose 1…

View original post 236 more words

Posted in Uncategorized | 2 Comments

Buy surgical mask online Singapore

Just bought this Dotafa (4-ply surgical mask made in Vietnam) mask from Qoo10.

The quality is good, with good thickness (see picture below). Delivery speed is fast as well (just 2 days using Qprime delivery). Only issue is the expensive price (around S$1 per mask), but that is the market rate nowadays…

The consensus is that made in Vietnam & made in Indonesia (3-ply or 4-ply) are the best options to get nowadays. This current batch may be the last batch since the respective countries are cracking down on the export of masks.



Photo of the “Dotafa” surgical mask (4-ply). There are other equivalent Vietnamese manufacturers as well on Qoo10.

See also:

Posted in Uncategorized | Tagged , , , | Leave a comment

Where to buy surgical mask in Singapore

This is an update to the earlier post: Where to buy surgical mask Singapore.


  • Basically, surgical masks are totally sold out in pharmacies like Watsons, Guardian, Unity, etc. Hand sanitizers are still in stock though, if you are interested to buy.
  • Korean masks on Qoo10 are mostly out of stock.
  • Currently, Qoo10 carries mainly Indonesian and Vietnam surgical masks, market price is around S$50 per box of 50 masks, i.e. around S$1 per mask.

The below Qoo10 shop (local stock) carries masks made in Indonesia and Vietnam masks (3 ply), with certificates. Basically, according to the reviews, the masks are genuine, only issue is that it is quite pricey. Apparently, the high price is set by the mask manufacturers and suppliers, it is not entirely the fault of the Qoo10 sellers that the price is so high. (Basic economics: High demand + low supply = High price.)




Example of certificate for made-in-Indonesia mask:

[S$29.90](▼58%)⏰⚡ [SG Ready Stock 16 MAR] Surgical Mask 3ply ★ OneMed Sensi Masks ★ Ship within SG n to Overseas


According to the above Qoo10 seller, the current batches would be the last batches as Indonesia has crackdown on export of surgical mask. Vietnam has also banned export.

Posted in Uncategorized | Tagged , | 1 Comment

Shrimp Videos

I find that shrimp are just as interesting as fish to keep in an aquarium. Shrimp are very good at tidying/cleaning up the aquarium; it is a great idea to keep some shrimp whenever possible.

The easiest shrimp to keep are cherry shrimp (and its color variants), and also the Amano shrimp. The biggest cause of shrimp deaths is due to molting problems. Below are some videos of the shrimp I have personally kept.

Easy to keep shrimp: Amano shrimp, cherry shrimp (Neocaridina davidi).

More difficult shrimp: Bamboo shrimp (aka Wood shrimp), Bee shrimp (I have not tried these yet), Sulawesi Shrimp (not tried yet either).

Posted in Uncategorized | Tagged , , , , | Leave a comment

AR Mini Low Tech Day 50

Read more at: Alternanthera Reineckii Mini Low Tech

Day 50 (12 March 2020): The aquarium light was upgraded around 10 days ago on 2 March 2020. It has helped the AR Mini in my opinion, making it slightly redder. The AR Mini is very much alive in the low tech tank! I think this dispels the myth that Alternanthera Reineckii Mini requires CO2 to live.

Posted in Uncategorized | Tagged , , , | Leave a comment

Ryo Watanabe Fish

In this video, popular fish YouTuber Ryo Watanabe is featuring the famous Clementi 328 (C328) Fish Store, arguably the best aquarium in the west (along with its neighboring shops in the stretch of Clementi Block 328).

Clementi Block 328 is my favorite fish store. Chances are very high that you can find whatever you are looking for in one of the shops in the stretch. Other than C328, other notable shops in the area include Polyart, and That Aquarium, and more.

Each store there has its own characteristics, they are unique in their own way (the fish/plants/equipment they carry are all different, it is clear they have different suppliers):

Polyart Clementi: Large collection of fish, including some saltwater. They do carry plants. Their equipment collection is very extensive, and notably they are cheaper than other Polyart outlets (the uncle will often give you a discount off the stated price without you even asking). I usually buy equipment/medication/anti-chlorine from this store.

That Aquarium: Features some of the more exotic fish (I once saw freshwater seahorses, aka pipefish) and shrimp (some black King Kong shrimp or similar that costs up to $100 per shrimp). They do have collection of a lot of “high class” food and equipment that may not be found in other shops.

C328 Aquarium (featured in Ryo Watanabe Fish Video): This store is crammed full of fish, plants and equipment. Notably, the plant section is more extensive than other shops in the Clementi 328 stretch, including frequent sightings of Bucephalandra and other rarer plants. Most of my plants are bought here.

LFS Aquarium: This store is the first fish store on the left. I have good experience buying their fish, so far their fish tend to be healthy without disease. They have good collection of nano fish, which I am interested in. For example, mosquito rasbora, lambchop rasbora are often spotted in their store. They also have Betta in their community tanks, which means that those Betta are proven to be less aggressive and can live with other fish.

Ryo Watanabe Fish Video

Ryo Watanabe also does Fish Videos in Japan, where he is based at currently. Ryo Watanabe’s fish videos center on freshwater fish, including aquarium plants and aquascaping.

Related posts:

Posted in Uncategorized | Tagged , , | Leave a comment

Pinterest Update

Previously, I tried using the automatic Pinterest RSS Feed but to no success. I even tried posting on the forum but again it did not address the problem. (To be fair, this is probably a problem on the Pinterest side.) Hence, the conclusion is that currently the to Pinterest automatic posting does not seem to work. (It apparently works for users according to my search on Google.)

Thus, I have manually added some pictures from Mathtuition88 (including reblogged content) onto Pinterest. Feel free to share it!

Manually adding pictures onto Pinterest is quite tedious and time-consuming. I will be monitoring how much effect Pinterest has, in terms of channelling traffic.

Posted in Uncategorized | Tagged , | Leave a comment

Free COVID-19 Insurance (DBS/POSB customers)

I looked through this free insurance by DBS, there seems to be no “catch” to it, i.e. it is really a 100% free insurance for you.

Maybe only “downside” is that you will have to provide your contact information which can be used by DBS/Chubb to “contact you via email, SMS and phone calls in respect of promotional offers”.

Sign up using the official link below.


  • Exclusive to DBS/POSB customers

    Free hospital income coverage for you and your family

  • Daily Hospital Cash Benefit

    Receive SGD 100 per day, up to 14 days in the event of hospitalisation due to COVID-19

  • ICU Hospital Cash Benefit

    Receive SGD 1,000 one-time lump sum payment, in the event of hospitalisation in ICU due to COVID-19

  • 30 days of free coverage

    Your cover starts immediately once you submit your application, and expires automatically at the end of 30 days

Posted in Uncategorized | Tagged , , | Leave a comment

The Secret of the Sweets (Sweet Distribution Problem)

Mrs Smith has some sweets to distribute to her students. If she gives each student 3 sweets, she will be left with 24 extra sweets. If she gives each student 5 sweets, she will be short of 42 sweets.

How many sweets does Mrs Smith have?

This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:

  • Homeschooling for gifted kids
  • Preparation for GEP (Gifted Education Programme) screening and selection tests
  • Preparation for Math Olympiad
  • Puzzles for kids interested in math but find school work too easy.


This is quite a tricky problem for Grade 2-4 students. The main problem is that the number of sweets, as well as the number of students is unknown! Many students will not know how to even start solving such questions.

We can reason as follows:

From 3 sweets each to 5 sweets each is an increase of 5-3=2 sweets each.

From having 24 extra sweets to being short of 42 sweets is a difference of 24+42=66 sweets.

Hence, to cause the above difference, there must be a total of 66/2=33 students!

Then, we can conclude:

33 students x 3 sweets each = 99 sweets

99+24=123 sweets altogether.

Answer: 123 sweets

We can also check our answer using another method:

33 students x 5 sweets each = 165 sweets

165-42=123 sweets.

Posted in Homeschool Math Challenging Puzzles | Tagged | 2 Comments

Anubias Rhizome tied too tight

Anubias tied too tightly

I think one of my Anubias rhizomes died (rotted) due to it being tied too tightly. The Anubias rhizome is supposed to be hard and green, if it is soft or brown, something is wrong.

For Anubias, the rhizome is the most important part of the plant, if it is dead, the whole plant will die.

Another reason for the Anubias rhizome rotting is the dreaded Anubias disease, but I don’t think it is the case here because another rhizome just next to the rotted rhizome is perfectly healthy.

Hence, the conclusion is that the Anubias rhizome most likely died from being tied too tightly by the string. It was at the back of my tank so I didn’t really notice it at first. I only noticed it when I saw a new leaf sprout out from the rotting rhizome, but the new leaf melted soon after. Usually, when new leaves melt, it is a sign of something wrong. Upon taking the entire Anubias plant out, I then realized that the rhizome had turned mushy.

The original Anubias was tied (by the seller) with thick string. I don’t really blame them for tying too tight because it is not easy at all to tie Anubias (too loose and it will not stay in place). I cut off the old string, threw away the rotted rhizome, and re-tied the healthy Anubias lightly with sewing thread.

Probably the same problem can occur for Java Fern, Bucephalandra, the rhizome may rot if tied too tightly.

Posted in Uncategorized | Tagged , , , , , , | Leave a comment

Hikari Shrimp Cuisine Review

I find this Hikari Shrimp Cuisine quite good. The pellets are quite small sized so you can control exactly how much you want to feed (down to each individual pellet).

Hikari Inc AHK19404 Shrimp Cuisine 0.35 -Ounce

How to feed Hikari Shrimp Cuisine Pellet (without fish snatching it away)

This was something that perplexed me for a long time. My fish would grab any food meant for the shrimp, leaving close to nothing left for the slower moving shrimp.

The solution I found was to:

  1. Put the Hikari Shrimp Cuisine pellets in a small container with tank water.
  2. Crush the pellets (I just use my finger).
  3. Stir to “dissolve” the pellets a little. Stirring also helps the pellets to sink.
  4. Pour the water with “dissolved” pellets back into the tank.

You may switch the order of steps 1 & 2 if you like (I find it easier to crush the pellets when wet).

The main reason why this works is because:

  • Hikari Shrimp pellets are sinking (this is very important since shrimp can only eat sinking pellets that reach the floor).
  • By crushing the pellets into powder, it is virtually impossible for the fish to snatch all the shrimp’s food.
  • Some, if not most, of the powder will reach the tank floor, where the shrimp can find and eat it.

Another way to feed shrimp exclusively is the usage of a shrimp feeding tube and feeding dish.

JZMYXA Shrimp Feeding Tube and Feeding Dish, Fit for Shrimp Fish, Mini Size, High Transparent Acrylic Material

How much Hikari Shrimp Cuisine Pellets to feed

This depends on how many shrimp you have, and also your tank setup. Ideally, shrimp such as cherry shrimp or Amano shrimp can survive on algae and biofilm. Hence, if your tank is well planted, you only need to feed lightly. Personally, I only feed the shrimps once a week, at around 2 Hikari Shrimp pellets per shrimp.

If your tank is bare (no plants), you need to feed more, maybe once every day or once every two days.

Supplementing with Hikari Shrimp food is good because it contains essential minerals like copper (shrimp need small amounts of copper) and other minerals that can help shrimp molt.

Posted in Uncategorized | Tagged , , , , , | Leave a comment

Toy Poodle Male Temperament

Just adopted a toy poodle (male). It is supposedly the 2nd most intelligent dog (after the Border Collie).

I was quite surprised that it is quite a well-behaved small dog, that seldom barks. It is currently 3 months, and only weighs around 1.5 kg.

Male vs female toy poodle temperament

Apparently, for poodles, it can often be the males that are more affectionate and loving and the females that are more dominant and challenging of authority. (Source:

Another poodle website source claims that “males tend to be more affectionate, playful, easier to house break and train, attentive and more demanding of attention. They adore their people and want to please. Most importantly if you have more than one person in your family, male dogs love everyone equally and share their affection with everyone. Female dogs tend to be a one person dog.”

Posted in Uncategorized | Tagged , , , | Leave a comment

Domain Authority 31

domain authority

Mathtuition88 has reached Domain Authority 31 (Moz DA).

Thank you to all who have ever linked to!

Posted in Uncategorized | Tagged , | Leave a comment

IMO Coach : Drill vs Think Style

Math Online Tom Circle

The USA IMO coach Prof Loh is the son of 2 Singaporean Math Prof (dad) & JC Math teacher (mom).
He uses the Chinese “drill” style + American “think” style to beat China IMO Team last few years.

View original post

Posted in Uncategorized | Leave a comment

The Great American Math Teacher 《Stand & Deliver 》

Posted in Uncategorized | Leave a comment

Silver Ratio, Bronze Ratio… A general “Golden Ratio”

Math Online Tom Circle

These 2 smart Singaporean students invented “Silver Ratio” , “Bronze Ratio” … equally good as the Golden Ratio.

Recap: Golden Ratio

View original post

Posted in Uncategorized | Leave a comment

Without Leap Year 29/2, Winter would become Summer

Posted in Uncategorized | Leave a comment

Music = Math + History

Math Online Tom Circle

To really appreciate music, you must understand this Math & history :
5 notes to 7 notes to 12 notes.
& fractions: 3/2, 3/4, 2/1 (octave)

Music = Math + History

1. Ancient China 600 BC 管仲 (5 notes 宫商角徵zhǐ羽)

2. Pythagoras 450 BC (7 notes, Chords 和弦)

3. Modern Music: 十二平均律 (明朝 1600 AD 朱载堉- > Bach 1700 AD)

Pythagoras did not believe in Irrational numbers (sqroot 2) , so only 7 integer notes.

17CE Chinese 明朝 Prince invented 12 notes music, using a giant 81-row Abacus to compute the12th root of 2 (picture below) :

View original post

Posted in Uncategorized | Leave a comment

Ideal in Ring

Math Online Tom Circle

Historical Background:

Ideal (理想) was a by-product by mathematicians in the 350-year proof of the 17CE Fermat’s Last Theorem, wherein they found a violation of the existing “Fundemental Law of Arithmetic” (Unique Prime Factorization) . Since it is a Law, there must be an alternative ideal number to satisfy it, hence the birth of the “Ideal”.

Read here: the raison d’être of Ideal : What is an Ideal ?


Why Integer (Z) is called “Ring” (Dedekind coined it using the German word “Der Ring”) ? because
{1, 2, … , 11, 12 = 0} is clock number “Z/12Z” like a Ring-shaped Clock 🕜


The ancient “Chinese Remainder Theorem” (aka 韩信点兵 ) since 200 BCE is explained by 19CE Ideal Theory.

[Solve] : “The Problem of 6 Professors

Whatever inside multiplies outside, still comes back inside.

View original post 54 more words

Posted in Uncategorized | Leave a comment

Stickers Math Question

Abby, Brian, Charles, Dennis and Eason have 50 stickers altogether.

Abby has the most stickers — she has 12 stickers.

In second place (tied) are Brian and Charles.

In third place is Dennis.

In fourth place is Eason, with 6 stickers.

How many stickers does Dennis have?

This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:

  • Homeschooling for gifted kids
  • Preparation for GEP (Gifted Education Programme) screening and selection tests
  • Preparation for Math Olympiad
  • Puzzles for kids interested in math but find school work too easy.

For this type of questions, the easiest way to do is “trial and error”, also known as “guess and check”.

Firstly, lets check how many stickers B, C, and D have together:


B C D Total (B+C+D) Comments
9 9 14 32 Wrong! Since D is more than A
10 10 12 32 Wrong! Since D is tied with A
11 11 10 32 Correct!
12 12 8 32 Wrong! Since B, C is tied with A

For guess and check, the most important thing is to be systematic, rather than guess wildly. For instance, we can systematically increase our guesses for B, C.

We can see that the only logical answer is:

B= C=11


Answer: Dennis has 10 stickers.

Posted in Homeschool Math Challenging Puzzles | Tagged , , | 1 Comment

What are some best hacks to switch careers?

Just saw this post on Quora. Reblogging it here in case the original post gets deleted.

Quite interesting advice, with a nice name of “monkey bar technique”.

My PhD advisor once gave me the advice to use the “monkey bar technique”.

If you have achieved success in field X, and want to move into field Y, then you really don’t want to have to go back down to the bottom again and have to work your way up. Instead, a better approach is often to use your skills in field X to get a job that allows you to build expertise in field Y.

Sometimes you might need to take several steps to get where you want, where in each step you use your current skills to get a job that allows you to build new skills. This is similar to the way a child moving across the monkey bars holds onto one bar while reaching out for the next one.

In my case, I started out with a PhD in programming language implementation, which led to a job as a research scientist at Intel where I learned about the web, which led to a job as a software engineer at Google where I learned about product design, which led to a job as a product manager at Google and then Quora.

Rob Ennals, Product Manager at Quora, Former PM at Google, Parent.


Posted in Uncategorized | Tagged , , | Leave a comment

Chai Discus Shop Tour by Ryo Watanabe

This Japanese boy Ryo Watanabe is currently based in Japan, but used to be in Singapore for some time (his mother works here). I think he is probably back in Singapore recently again based on his videos.

Very amazing discus fish store tour. I usually enjoy watching his videos during meals, I think I have watched almost every single video (except those super long video interviews which may be more than an hour).

Do subscribe to his channel, and like, share, etc. His videos are usually very professionally produced, and he speaks very good English. Sometimes, I wish I have the time to tour all the fish stores like him.

SG Bearded Aquarist Fish Videos

Another fish YouTuber based in SG is SG Bearded Aquarist. Currently, he seems to be “inactive” for quite some time, maybe working on a new project? His videos are also very professionally produced, and he does branch out to overseas aquariums/ saltwater/ planted tanks as well.

One of my favorite videos from SG Bearded Aquarist is the one below (featuring Zaric and Jarenn Foo who are expert Pleco breeders).

Posted in Uncategorized | Tagged , , , , | 3 Comments

How to turn your blog into a book

This is something quite interesting. Possibly a very good idea for many bloggers — kill two birds with one stone (write a book while developing a blog).

Source: How to turn your blog into a book (WordPress)

We know many of you love your blogs, and gleefully publish photos and posts without thoughts to reuse your work in other forms. But we know some wonder: could this be a book? Recently we wrote about how a blogger scored a book deal for You Are Not So Smart. But what if you want to do it all yourself?

As a blogger who has authored several successful books with publishers, and who works on, I recently self-published a book based entirely on posts from my blog. I wanted to see what I could learn, and I’m here to share it all with you.

The book I self-published is called Mindfire: Big Ideas for Curious Minds. It’s a collection of my best essays from my WordPress blog at, where I write about ideas, creativity and leadership. The book has done well, and has often been in the top 100 books on philosophy and other categories on amazon since it was published.

There are four questions I often get asked by other bloggers.

1. How do you shape a blog into a book?

This is the wrong way to start. A book is a different reading experience than a blog, and to “shape” a blog into a book assumes words are like clay, where you can shove them into any shape you like. A book is a longer reading experience, and every chapter, or every page, needs to line up in a readable way with the others. It will take some effort to rework  material written for a blog to fit well together as a book. Don’t start with the assumption you’ll include every single post on your blog, or keep them in the chronological order they were written.

The first step is to make two lists: possible posts and possible concepts. You might discover a book concept that’s strong, but you only have 10 or 12 posts that fit. That’s ok. You can always choose to write more. Of course the theme of your entire blog could be the theme for a book, but consider other concepts too.

I went back to the beginning and made a list of posts that might be good enough to include. I made a separate list of possible book concepts. One concept I saw in some of my posts was intelligent provocation: asking big questions and offering intelligent and entertaining answers. I filtered the list based on that concept, and arrived at 45 possible posts.  Then I hired an editor to help refine the list, and the result was 30 posts that, while all written independently, fit together into an excellent read.

There are services like Blurb or Blog2print that will take your blog and build a book from it. If your WordPress blog is self-hosted, and not on, you might take a look at Anthologize, a plugin that automates the process of converting your blog into an e-book. But these services do nothing to shape your work into a great read. No software can do this for you.  There is an enormous distance between a ‘book’ and a ‘book someone will enjoy reading’ and that distance is closed only by your hard work.

Plan to take a draft version of your book and ask people to read it. Ask for feedback on improving the order of posts, or which posts don’t fit. You’ll notice people expect tighter and more careful writing in a book, compared to reading posts online. It’s acting on this feedback that makes the difference between a book that feels like a book, and a book that feels like a bunch of random posts thrown together. Revise posts, or write new material, to develop the book into a singular strong narrative. I asked for volunteers on my blog for people to give feedback on the drafts and their input was a key part of making the book so strong.

2. How do you actually (self) publish a book?

To go the traditional route, you’ll need to reach out to publishers or agents and try to find one that’s interested. This takes significant effort beyond writing the book itself. In all cases, traditional or self-published, the hardest part is writing and editing an excellent book. If you’re dedicated to your book, self-publishing can allow you to focus your energy on making the book better, rather than in searching for someone to give you a chance you can give yourself.

If you already have a well edited manuscript, you are most of the way there: the technical parts of self-publishing are surprisingly easy. You take your complete manuscript, after it has been copyedited and reviewed by an editor, and convert it to a PDF. With a PDF in hand, there are many services that will convert your PDF to a print or digital book for you.

For Mindfire, I used Lightning Source for the print edition, and a service called BookBaby to manage the digital editions.  These services list the book on, and it can be purchased like any other book on, including KindleiBook and other digital versions. It doesn’t cost much: maybe a few hundred dollars. If you choose to only produce a digital version, it can be much cheaper.

The more work you do, the cheaper the services are. If you are willing to hire your own editor and cover designer, or do those tasks yourself, and take care of details like getting an ISBN number, you can user services like  Lightning Source or CreateSpace to simply print and distribute he book. But if you want to hire people to help you, services like CreateSpace and let you pay them to take care of many steps on your behalf.

3. Why would people buy a book if the content is free on the blog?

The rise of the iPad and Kindle have proven the demand for longer reading experiences, experiences longer than what the web provides. A compilation of your work offers a deeper experience than what people get through your blog alone. Blogs are fantastic for small to medium length reading experiences, but to consume 40 or 50 posts without interruption, posts that are chosen to fit together on a specific theme, you need something else. A book is a better experience for this kind of continuous reading.

A book gives you an object demonstrating your talents to potential clients, business partners or anyone in the world you wish to impress. Since a book is often perceived as being a greater accomplishment than having a blog, it can be a stronger invitation to a new reader to give your work a try. It also allows your fans and friends to buy copies of your book to give to their friends as gifts: it helps them help you spread word of your work.

4. How can I use my blog to help the book succeed with the book?

If you involve your readers as your produce the book, they will naturally help spread word when it’s done. Using polls I asked my readers to help pick the title, to give feedback on several rounds of cover designs, and many other decisions. This attracted new readers curious about how books are made, and allowed me to collaborate with my readers on the book, increasing their interest in seeing it finished and released.

It’s counterintuitive, but giving the book away for free for a time helps a new book, and your blog, tremendously.

First it rewards your regular readers – who deserves a free copy more than your regular readers? The free give-away helps enlist them to reach out to their networks to bring more people to your blog for the first time. I gave Mindfire away for free for 48 hours, and had over 10,000 people download the book. It’s true my blog is popular, but many of those downloads were by people who had never heard of me before. My great fans on my site helped spread word on twitter and Facebook of my free offer, spreading my reach for future blog posts and books. I still give 1/3rd of the book away for free as a preview for anyone who wants to give it a try.

5. What’s the first step to take?

You’re a blogger: start by blogging about it. Ask your readers if they’re interested in helping you work on a book. Post your list of book concepts and see what they think. Perhaps there’s an author, editor or designer who reads your work that can lend their expertise. Take a careful look at the work you’ve already written and start thinking about what concepts might match.

Quote | Posted on by | Tagged , , , | 2 Comments

Marbles Math Question

Aaron and Bob had some marbles in a box.

At first, Bob had thrice as many marbles as Aaron.

Aaron sold 5 marbles and Bob bought another 35 marbles.

Then, Bob had 5 times as many marbles as Aaron.

How many marbles were there in the box at first?

This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:

  • Homeschooling for gifted kids
  • Preparation for GEP (Gifted Education Programme) screening and selection tests
  • Preparation for Math Olympiad
  • Puzzles for kids interested in math but find school work too easy.


This question can be solved using the “units” method, and “working backwards”.

At the end, Bob had 5 times as many marbles as Aaron.

We write:

Aaron –> 1u

Bob –> 5u

Next, we work one step backwards (before Aaron sold 5 marbles and Bob bought another 35 marbles.)

Aaron –> 1u + 5

Bob —> 5u – 35

Now, we calculate what is 3 times of Aaron (thrice of Aaron’s marbles):

3 times of Aaron –> 3u + 15

We can conclude that:

3u+15 = 5u-35

We may draw the above model, after which we can conclude that:

2u –> 15+35=50

1u —> 25

Hence, Aaron had 1u+5 = 30 marbles at the start.

Bob had 5u-35 = 90 marbles at the start.

In total, there are 30+90= 120 marbles at first.

Ans: 120


Posted in Homeschool Math Challenging Puzzles | Tagged , | 1 Comment

Homeschool Math Challenging Puzzles

Homeschool Math Challenging Questions

Mathtuition88 will be starting a series of Homeschool Math Challenging Problems, aimed at age 8 to 10 (Grade 2 to 4).

This series is targeted at kids age 8 to 10 who are strong / gifted at mathematics and wish to further stretch their potential. It is also useful for children who may not be strong in math at the moment, but have a keen interest in math nonetheless.

In particular, it is very suitable for the following purposes:

  • Homeschooling for gifted kids
  • Preparation for GEP (Gifted Education Programme) screening and selection tests
  • Preparation for Math Olympiad
  • Puzzles for kids interested in math but find school work too easy.

This series of questions will follow the Singapore Math syllabus for Grade 3 students, covering the following topics:

  1. Whole Numbers
  2. Fractions
  3. Money
  4. Measurement (Length, Mass, Volume)
  5. Time
  6. Area and Perimeter (rectangle/square)

Although the syllabus above is elementary, we are choosing the toughest math questions (while still remaining in the framework of the syllabus). Hence, the title of the series is “Homeschool Math Challenging Puzzles for Grades 2-4”!

As far as possible, the questions will be categorized under:

Posted in Homeschool Math Challenging Puzzles | Tagged , , , , | 13 Comments

7 Essential Abilities To Be A Successful Entrepreneur 

7 Essential Abilities To Be A Successful Entrepreneur 

Destination wanted by anyone who opens their particular company is a success.  However, despite the same objective, entrepreneurs can achieve success by taking very different paths. Regardless of the differences. Some values are typical of the huge majority of successful entrepreneurs. However, different from the profile of everyone is. Several training courses such as HR training courses, personal development courses, administration courses etc are conducted by Zoe Talent Solution. These courses help you to increase the growth of the business and helps to run the business successfully.

  1. Ambition

Without the desire to grow, achievement becomes more difficult.  To be ambitious is to have courage, firmness, and accept challenges, which means leaving your comfort zone.  Many views, that this value as something negative, possibly because they imagine that ambitious individual may harm others to reach their objectives, which isn’t correct. There’s absolutely no such lack of scruple.  What there is is an excellent instinct for competitiveness and a willingness to lead.

  1. Control

Achieving success isn’t straightforward.  Until everything goes well, lots of people get into debt, it takes time to construct a fantastic team and suffers to entice customers, among some other issues.  And, it isn’t easy to go through bad times without psychological control to withstand that pressure. The entrepreneurs must be willing to take risks.  If you want a more predictable life, maybe owning a business isn’t the best means for you.

  1. Perseverance 

Another important element that stands out in many lists of essential ingredients in the entrepreneur’s profile is perseverance.  Without that determination, you give up at the first sign of crisis.  So it’s important to believe that however long it takes you’ll get along.

  1. Be sociable.  

Whoever has their own business should relate, at all times, with clients, employees, and suppliers.  Therefore, extroverts have a certain advantage.  However, this doesn’t necessarily mean that shy people don’t stand a chance when undertaking.  They simply have to surround themselves with people that are good at interpersonal relationships.

  1. Being a revolutionary is not compulsory 

We often associate the image of the entrepreneur with that of the inventor that transforms a brilliant idea into a unique and disruptive business.  But, according to Santos, the entrepreneur isn’t always an inventor.  They could do very well when perfecting a product, or improve the processes of creating something.

  1. Relationship Building

Building relationships in business are essential for entrepreneurs because powerful relationships are required to resist persistent anxieties.  Relationships with colleagues, suppliers, clients, investors and a high number of different stakeholders are important. Great relationships that are maintained over time demand a whole lot of work and a great deal of skill.  Having a fantastic relationship focuses on trust, and if it is possible to create a sense of confidence in yourself and your business, this is going to be quite helpful. Concentrate on creating situations where everyone wins and ask yourself how I can improve things for another person is a handy way to build relationships and trust.

  1. Continuous self-development 

Those working in large companies are frequently asked to take part in the training.  Ideally, when you tackle, you continue to”train” your mind.  We are living in a world where everything changes very quickly and you will need to be always current.

Posted in Uncategorized | Leave a comment

Going Hungry In Singapore

Singapore is famous for its cheap hawker food, including the cheapest Michelin-starred meal in the world. Why does hunger, or food insecurity, still exist in this city?

Food insecurity refers to the lack of reliable access to nutritious food due to financial constraints. But we found that it doesn’t exist only among the lower-income or the elderly poor. In a two-part special, CNA Insider investigates the issue of hunger, and the efforts to address it in Singapore. We spent months talking to recipients of food aid, and groups like The Food Bank Singapore, Free Food From All, Food From The Heart, Keeping Hope Alive, Willing Hearts, Volunteer Switchboard and SG Food Rescue.

Read more: Why some are going hungry in a cheap food paradise

How you can donate or volunteer:

Food From The Heart:

Food Bank Singapore:…

Free Food For All:

Willing Hearts:

National Volunteer and Philanthropy Centre:

TOUCH Community Services: To volunteer for Meals-On-Wheels delivery, call 68046565

Posted in Uncategorized | Tagged , , , | Leave a comment

GEP Test Format

There is limited information on the GEP Test Format on the official MOE website:


The entry point into the GEP is at Primary 4.

Pupils are identified for the GEP through a two-stage exercise in Primary 3.

Stage Month Participants Papers
Screening August Primary 3 pupils enrolled in government and government-aided schools English Language


Selection October Only shortlisted pupils will be invited to the Selection stage English Language


General Ability

For the screening test, the duration for each paper is around 1.5 hours.

For the selection test, there are traditionally two papers of 2.5 hours each:

  • Paper 1: English paper and a General Ability paper
  • Paper 2: Maths paper and another General Ability paper

In August every year, the cohort of P3 students is invited to sit for a GEP screening test. The test is not compulsory but all children are encouraged to go for it. The test comprises an English and a Maths paper, about 1½ hours each.

Out of the cohort of approximately 50,000 kids, some 3,000 pupils (about 6%) are shortlisted for the GEP selection test.

The selection test takes place over two days in October, the first comprises an English paper and a General Ability paper, about 2½ hours in total. The second consists of a Maths paper and another General Ability paper, also about 2½ hours altogether.


GEP Test Syllabus

Officially, the GEP Test can only test within the Primary 3 syllabus. (This is more relevant for Math than English. For English, it is more open-ended, they can test advanced GEP vocabulary like “cantankerous”.)

For example, technically they are not supposed to test “speed” questions since that is a Primary 5 topic. Similarly, they are not supposed to test area/perimeter of circle questions, or even area/perimeter of triangle questions.

Hence, the GEP Math Test Syllabus (according to the official Primary 3 syllabus) includes:

  1. Whole Numbers
  2. Fractions
  3. Money
  4. Measurement (Length, Mass, Volume)
  5. Time
  6. Area and Perimeter (rectangle/square)
  7. Angles (basic concepts of right angle, acute angle)
  8. Perpendicular & Parallel Lines (basic concepts)
  9. Bar graphs

The above topics may seem deceptively easy. However, even for a simple topic like fractions, it is possible to test a question like the GEP Screening Test Question Sample: The Tap Question, which may stump many secondary school students.

Related posts:

Posted in Uncategorized | Tagged , , | Leave a comment

The Notorious Collatz conjecture

Terence Tao has uploaded his slides on the Collatz conjecture (targeted at high school students):

A very enjoyable read indeed.

The best “encyclopedic” reference on the Collatz conjecture is the one listed below, published by the American Math Society. Note that the Collatz conjecture remains unsolved as of today.

The Ultimate Challenge: The 3x+1 Problem

Posted in Uncategorized | Tagged , , | Leave a comment

Pinterest RSS Feed

Just testing my Pinterest RSS Feed. Set up a Pinterest account long ago but did not use it. Apparently Pinterest is useful for SEO, even more useful than Instagram which is mainly for branding. This is because Pinterest has backlinks pointing back to your original website.

Pinterest URL:

For testing, I will just upload this logo created using a free logo maker (

Mathtuition88 Logo

Connect RSS feeds to your Pinterest business account and automatically create Pins from the content on your website. When you update your RSS feed, your content will be added to your boards as Pins within 24 hours.


Update: I am facing this error, which I have no idea how to solve…

Oops! It looks like some of your connected RSS feeds are failing. Please review the errors below:

Pinterest can’t find images in your feed. Please make sure your feed has high quality images in <enclosure>, or <media:content> tags under each <item> tag.

Please check our Help Center for further details or to get help troubleshooting.

Posted in Uncategorized | Tagged , , , | 6 Comments

The Wisdom Of The Law – Homily by Archbishop William Goh (16 Feb 2020)

Due to the COVID-19 virus, all Catholic masses in Singapore are suspended (till further notice). A YouTube online mass is made available.

Posted in Uncategorized | Tagged , , , | Leave a comment

Preparation Tips for Examination For MBA

Preparation Tips for Examination For MBA

The preparation for the CAT exam 2020  is slightly different for the type of aspirants appearing. It has a division into two sections:

For first-time appearing aspirants Sol du Admission :

If you are going to attempt the CAT exam preparation tips for the first time, you can start with a full-time online course.

In this, the examining faculty will keep you updated about every aspect or changes in the CAT exam.

  • They will also help you to better and efficiently understand the techniques, tips, and tricks of solving the question paper.
  • The online course providers will also offer you study material and mock tests to assist you in your preparation.
  • After completing your syllabus, you can take revision classes and doubt classes to clear all the concepts of the exam.


Career counseling in India



 For reappearing aspirants:

If an aspirant fails to clear the CAT exam in the first attempt, he/she shouldn’t feel disheartened. Instead, give yourself another chance and start your preparation again after making a few changes.

  • Firstly, analyze your weak and strong points in the syllabus.
  • You can also take sectional tests available online.
  • Try giving more and more mock tests to improve your practice score. Also, make sure you solve the previous year question papers of CAT.
  • Make sure you give a minimum of 3-4 hours per day for the exam.
  • Be consistent in your preparation. An aspirant needs at least 7-8 months of training to score well in the CAT exam.

You can always change the exam preparation plan according to your strengths, weaknesses, and capabilities. There are no fixed preparation criteria to clear the exam.

 Application Fee

The application fee for general or OBC category students is INR 1900, while for the reserved category students (SC, ST, PWD), the fee is INR 950.

Admit Card

The admit card for the CAT exam will be available on the official website. The tentative date set for the availability of the admit card in October.

  • Aspirants who have submitted their applications successfully can download the admit card by logging in to their account.
  • After downloading the admit card, make sure all your details and information mentioned on it is correct.
  • If there’s any mistake, contact the concerned authority to get it changed.
  • If your admit card is fine with all the details, get a printout of it and make sure you carry it while going for the CAT exam.

Exam Date

The tentative date set for the conduct of the CAT exam is the month of November.

 Exam Results

The results of the CAT exam expected a declaration in January. They will be out on the official website only.

 Exam Centre

CAT will get conducted in a total of 156 cities across India. It will hold in two different slots- morning and evening.

Posted in Uncategorized | Leave a comment



The entry for the CPL course in IGRUA involves the selection process, which begins with the Online Written Exam (Computer-based), followed by the Interview Round and lastly the Pilot Aptitude/PT. To take an entry, aspirants are mandated to qualify every stage of the Entry process. Aspirants qualifying the Online Written Exam will call in for the Interview Round. Following the Interview Round, the selected aspirants will further get notified for the PAT.

The entry for CPL will get done based on the marks scored by aspirants in the PAT.

Some of the students those need to take admission in kuvempu university

Career counseling in India

  •         IMTS INSTITUTE ( NOIDA )

Exam Pattern:

  • Online Written Exam-The question paper comprises Mathematics, General English, Physics, Reasoning, and Current Affairs.
  • There is no negative marking.
  • The question paper consists of 10+2 level objective-type questions.
  • The cut-off for reserved category aspirants is 5% less than the score obtained by the last General category aspirant.
  • Interview Round- The aspirants shortlisted for the Interview Round are required to bring in the following documents for verification:
  • Birth Certificate (10th Class certificate)
  • 10th Mark sheet
  • 10+2 Mark sheet
  • Caste certificate for reserved category aspirants
  • Admit Card downloaded for Online Written Exam
  • PAT / PT- The aspirants qualifying the Interview Round will move on to the PAT. The reserved category students will not be allowed any relaxation for the Pilot Aptitude / PT. Qualifying the PT will make the aspirant eligible for entry in CPL.

Official website

Aspirants recommended visiting the official website of the IGRAU institute for any information regarding the Entrance Test at The applying aspirants can also download their Admit Card for the Online Written Exam through the official portal referred to above.

Frequently Asked Questions (FAQs):

Q how can i take admission in Assam Don Bosco University

A you can visit university website 

  1. In which cities is the Online Written Exam conducted?
  2. The IGRUAconducts the Online Written Exam in all the major cities across the nation. The relevant address about the centre, prescribed in the Admit Card.
  3. What is the minimum age for joining the CPL course?
  4. The aspirants must not be below the age of 17 years for joining the CPL course. Aspirants below 17 years of age can apply for the selection process positively.
  5. What is the limit for intake of entry for the CPL course?
  6. The IGRUA selects a maximum of 100 aspirants annually for the course.
Posted in Uncategorized | Leave a comment

Mosquito Rasbora & Neon Tetra

Mosquito Rasbora (Boraras Merah / Phoenix Rasbora) can live peacefully together with neon tetras!

The neon tetras mostly ignore the smaller mosquito rasboras, except maybe during feeding time where they try to snatch the food. There has been zero aggression between the mosquito rasboras and the neon tetras.

Mosquito Rasbora are surprisingly clever and have distinct personalities. One of my mosquito rasbora prefer to hangout near the top of the water together with the neon tetras, while another prefers to swim low near the roots of plants.

Mosquito Rasbora together with Neon Tetra

Phoenix Rasbora with Neon Tetra in the background (behind leaf)

Boraras Merah (Phoenix Rasbora) is a micropredator and a surprisingly intelligent small fish.

Posted in Uncategorized | Tagged , , , , | 1 Comment

Should I fast my fish once a week?

Many aquarium hobbyists propose fasting their fish once a week (i.e. not feeding the fish one day every week). The benefits of doing so include:

  • lower chance of constipation / bloating which may lead to swim bladder disease
  • clear the digestive system
  • better water quality (this is not the main point, but a side benefit)

I think in part people fast fish because in nature, if the fish was living it’s natural life, it would never be able to count on finding food every day, so fasting now and then is seen to be more in keeping with a natural life. Living in a glass box is so far from nature I’m not sure how valid that reasoning is, but it does no harm.

Man made foods are also filled with things the fish would never, ever eat in the wild, so fasting may be a break from some of that. Might be better to alternate man made with frozen or live though, the fish will be healthier for it.

If a fish has been constipated, fasting may well give the bowel a needed rest. Man made foods have many things like flour and other binding or bulking agents, and they are, I think, one of the prime reasons some fish become constipated. It’s not what they evolved to eat.

Just for an example, feeding living daphnia in quantity to fish is almost like giving them a laxative, they shoot through so fast, but fish eating living daphnia have amazing colour and vitality too. Great for conditioning to breed. In the wild daphnia are rather ephemeral, having huge numbers in spring and far fewer later. So fish and other critters that eat them, eat them much like we do some of the more perishable fruits.. when they’re available ! They eat all they can ’til they’re gone.


There is also a scientific research article on fasting tilapia fish. Basically the study found that “Overall, results suggest that fasting one day a week does not affect growth efficiency and that tilapia adjust well to relative changes in feeding frequency.”

Posted in Uncategorized | Tagged , , | Leave a comment

What is 8 ÷ 2(2+2) = ?

The correct answer, according to New York Times, is 16!

The other popular answer is 1.

The main idea is to use the BODMAS rule, to evaluate the bracket first. Then, it becomes 8÷2×4 = 4×4 = 16.

Posted in Uncategorized | Tagged , | 1 Comment

Jeff Bezos: How do you say no to annoying meeting requests?


How do you respond:

  1. A) Yes, I’ll definitely meet with you.
  2. B) No, I won’t meet with you.
  3. C) Tell you what. Call so and so and they’ll work something out.
  4. D) Quietly resolve to become a shut-in.
  5. E) Something else (fill in the blank)

Quite interesting to see Jeff Bezos’s answer (Option C).

Unfortunately this option only works for higher level executives who have a secretary/admin staff?


Posted in Uncategorized | Tagged , , , | Leave a comment

Python (Anaconda) does not work with MacOS Catalina!

This is just to highlight that the Anaconda Python Distribution does not work with the latest MacOS Catalina. I only realized upon trying to open Anaconda Navigator, after installing Catalina.

The only (good) solution seems to be reinstalling Anaconda.


MacOS Catalina was released on October 7, 2019, and has been causing quite a stir for Anaconda users.  Apple has decided that Anaconda’s default install location in the root folder is not allowed. It moves that folder into a folder on your desktop called “Relocated Items,” in the Security folder. If you’ve used the .pkg installer for Anaconda, this probably broke your Anaconda installation.  Many users discuss the breakage at

Posted in Uncategorized | Tagged , , , , | Leave a comment

LaTex Plot Axis 3D

There are many packages in LaTeX to plot 3D, including tikz-3dplot, and other exotic packages.

The easiest one to use for plotting a simple 3D graph, with xyz axis and origin, is Pgfplots in my opinion.

The code to plot the diagram below is included for reference.

First, we need to add the following in the preamble of the LaTeX document:


Then, to draw the actual diagram, the following simple code will do:

  axis lines=center,

% plot dots for the points
\addplot3 [only marks] coordinates {(1,2,3) (4,5,6)};

% plot dashed lines to axes
\addplot3 [no marks,densely dashed] coordinates {(1,2,3) (4,5,6)};

% label points
\node [above] at (axis cs:1,2,3) {$A (1,2,3)$};
\node [above right] at (axis cs:4,5,6) {$B (4,5,6)$};
\node [below left] at (axis cs:0,0,0) {$O$};
Posted in Uncategorized | Tagged , , , , | Leave a comment

Neon Tetra Bloated

Neon Tetra Bloated (Constipation)

One of my neon tetras is bloated/constipated. It has trouble sinking, it is swimming heads down and tails up. Hopefully it does not progress to the dreaded swim bladder disease or dropsy. Possible reasons is that it could have eaten the lion’s share of the TetraMin flake food the day before. I tried dosing Melafix (do not have any other suitable medication). I find that flake food tends to make neon tetras bloated (they may swallow air at the surface), but usually it subsides within a few hours. This tetra has been bloated for one full day, which is quite abnormal according to my experience.

Neon Tetra Bloated Recovery

Good news! The neon tetra recovered from bloat! Its stomach is noticeably more normal sized (previously there was a small lump). I am not sure if it was due to the Melafix or not. It is swimming normally now.

Update: I found out that one way to prevent neon tetra from getting bloated, without pre-soaking pellets and flakes, is to scatter the floating pellets in a wide area around the tank. This allows more time for the pellets to absorb water while the neon tetras are searching around. I found that this is much better than feeding through the “feeding slot” area at the top of my tank lid.

Another advantage is that slower fish can also get a better chance at eating the pellets while the fast neons are swimming around searching for their food. If I drop the pellets in a small area, it is likely that a few neon tetras will gobble up all the food, leaving none for the rest (and those neon tetras will end up bloated).

Posted in Uncategorized | Tagged , , | Leave a comment