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.
  • PSLE challenging Math problem sums. The questions are also well within the PSLE Math Syllabus, and will be challenging to Primary 6 students as well.

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:


Story of Yunhao Fu, 2-time IMO Perfect Scorer

Those who are acquainted with IMO (International Math Olympiad) would know that it is extremely tough to get a gold medal (in fact any medal at all) in the IMO. Fu Yunhao, from China, scored 42/42 perfect score twice in a row. His record can be viewed here. IMO’s difficulty varies from year to year. Fu Yunhao’s two attempts were during “difficult” years, hence he may be one of the best Math Olympians in the history.

However, his life story is quite unique in the sense that after his IMO triumph, things did not go quite smoothly. The below interview (unfortunately only in Chinese) describes it:

Google Translate of interview: English Translation


“The two-time Olympic champion” – although not accurate enough, it also summed up the highest achievements in the first 33 years of Fu Yunsheng’s life: he was the IMO (International Mathematical Olympiad) 2002 and 2003 two consecutive years of full-time gold medalist . In the 30-year history of the Chinese national team, only three players have achieved this result. IMO has the difficulty of being “relatively difficult” and “relatively simple.” Fu Yunyi is the only Chinese player who has competed for two “relatively difficult” matches. The Education Authority of China, Zhu Huawei, commented on Fu Yunxi: “He is a symbol of the Chinese mathematical community.”

To some extent, young people who are qualified to embark on the battlefield of IMO can represent the most outstanding mathematics mind of the generation. Professor Yakovlev, a former communications academy of the Soviet Academy of Sciences and a former chairman of the two-year IMO, made famous assertions: “Now the participating students will become the laborers who hold the golden key of knowledge and wisdom in the world 10 years later. they.”

Most of the IMO contestants will continue to engage in mathematics research in their adulthood. Among the 14 winners of the Fields Prize (recognized as the “Nobel Prize in mathematics”) since 2000, at least 8 of them have IMO’s record. But Fu Yunjun, the much-anticipated Olympic genius who once occupied the high point of IMO, unexpectedly disappeared in academia for the next fifteen years.

Some netizens came up with an old post titled “Fu Yunyi, First Class Cowman”, and asked for advice on the status quo of Fu Yunyi. Like igniting curiosity, those who have heard of their reputation have asked each other in the bottom: where is Fu Yunyi going?

(“Cowman” 牛人 means someone who is really good and excels in doing something.)

(Due to some translational errors, different spelling versions of Fu Yunhao’s name appear. They are all the same person, Fu Yunhao.)

However, the published interview does not reflect the full story. Fu himself posted a follow-up post here: Basically, Fu argues that not following the traditional path of becoming a top mathematician does not mean that it is a failure; on the contrary his chosen path (lecturer at teacher’s college) benefits society by producing more good teachers to teach more students.

Google Translate of Fu’s follow-up post: English Translation

Excerpt: The third reaction: Incomprehension of the values ​​conveyed by the report. According to the author of the article, the point is: Excellent people are engaged in basic work and it is a very shameful thing. Those who have won the imo championship are, if nothing else, their journey must be the sea of ​​higher mathematics instead of teaching a group of “second normal school students” to teach junior high school mathematics knowledge. Two of the normal students who lectured said that the genius had fallen. Although I denied that I was a genius, I still thanked Wu for collecting my example of genius. He is very hardworking and commendable. However, the negative energy brought by his values ​​has forced me to vocalize. I didn’t speak for self-explanatory innocence. I just sang for the positive energy development. First of all, for the Wu students who wrote such values, I expressed my understanding that the author, as a senior student who has not completely taken the ivory tower, has such an idea that it is normal. In his cognitive system, academic research is the top grade, ordinary work is relatively low, and lectures are given to two normal students, and it is even closer to the center of the earth. If a once successful genius did not make achievements in heaven and earth, but lived aliciously, it was failure! In Wu’s report to me, this tendency was obvious during the interview. In an interview on April 1st, I even put forward an example of Mr. Zhang Yitang to mention him. At the same time, I mentioned that many researchers have strong academic abilities, but they always go the wrong way, and they have never been able to conquer their life. Want to overcome the problem, but they are still happy and fulfilling. Those things that I spent 10 days and a half wanting to understand may not be of great value, but how many are some interesting conclusions. Moreover, aside from the results of the research, the process of research itself is a happy thing. Although the author did not ignore this paragraph, I mentioned it slightly at the end of the article, but in his eyes, I would like to give this example in order to balance my talent from the genius champion to the teacher of the “Second Normal School” in front of the interviewer. Heart drop it. However, I do not have such a psychological gap. Young people experienced academic crackdowns, and there were some gaps during the very decadent period, but these have been resolved. For so many years of work and life, I learned that there is a vast world beyond the University’s ivory tower and there are so many things waiting for people to practice. If you have a halo above your head and you are in a high tower, you may be able to refer to the country and spur words, but only if your feet are implemented and everything is done well, you can accumulate less and contribute more to the community. Two of my teammates who were with me in 2003, two of them are still swimming in the sea of ​​mathematics, and the other three are involved in the financial industry, which I mentioned in the interview. Each of them did not regret his choice, nor did I.

If you are interested in Olympiad books, check out Recommended Maths Olympiad Books for Self Learning / Domain Test.


We show how to solve “Clock” olympiad questions, which appear often in APMOPS/ SMOPS Olympiad questions.

Question: (SMOPS 2001, Q9)

Between 12 o’clock and 1 o’clock, at what time will the hour hand and minute hand make an angle of 110 degrees?

Full Solution:

We first analyse the hour hand:

It takes 60 min for the hour hand to move 360/12=30 degrees.

30 deg — 60 min

1 deg — 60/30=2 min

x deg — 2x min

(We measure the degree from the 12 o’clock vertical position.)

Next we analyse the minute hand:

It takes 5 min for the minute hand to move 30 degrees.

30 deg — 5 min

1 deg — 5/30=1/6 min

(x+110) deg — (x+110)/6 min

Now, we want the hour hand to be at x deg, and the minute hand to be at (x+110) deg simultaneously:





Since x deg — 2x min, hence the answer is

2x=20 min after 12 o’clock

Ans: 12.20

Math Olympiad Tuition

Maths Olympiad Tuition

Tutor: Mr Wu (Raffles Alumni, NUS Maths Grad)


Syllabus: Primary / Secondary Maths Olympiad. Includes Number Theory, Geometry, Combinatorics, Sequences, Series, and more. Flexible curriculum tailored to student’s needs. I can provide material, or teach from any preferred material that the student has.

Target audience: For students with strong interest in Maths. Suitable for those preparing for Olympiad competitions, DSA, GEP, or just learning for personal interest.

Location: West / Central Singapore at student’s home

A Graph Theory Olympiad Question Whose Answer is 1015056

April’s Math Olympiad Question was a particularly tough one, only four people in the world solved it! One from Japan, one from Slovakia, one from Ankara, and one from Singapore!

The question starts off seemingly simple enough:

In a party attended by 2015 guests among any 7 guests at most 12 handshakes had been
exchanged. Determine the maximal possible total number of handshakes.

However, when one starts trying out the questions, one quickly realizes the number of handshakes is very large, possibly even up to millions. This question definitely can’t be solved by trial and error!

This question is ideally modeled by a graph, and has connections to the idea of a Turán graph.

The official solution can be accessed here:


Turan 13-4.svg
The Turán graph T(13,4)


To read more about Math Olympiad books, you may check out my earlier post on Recommended Math Olympiad books for self-learning.

Discriminant of Quadratic Polynomial Olympiad Question

The discriminant of a quadratic polynomial (b^2-4ac) is a source of confusion for many students taking O Level A Maths. After explaining, students usually will understand the concept, but it remains really tricky. It is a really useful concept, and can be used here in this Math Olympiad Question:

Question: bilkent nov question



One of the above people who answered correctly, Toshihiro Shimizu, is an IMO Gold Medalist from Japan.

Featured Book:

Mathematical Olympiad Challenges

Highly Rated on Amazon!

Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory

Historical insights and asides are presented to stimulate further inquiry

Emphasis is on creative solutions to open-ended problems


JC Junior College H2 Maths Tuition

If you or a friend are looking for Maths tuitionO level, A level H2 JC (Junior College) Maths Tuition, IB, IP, Olympiad, GEP and any other form of mathematics you can think of.

Experienced, qualified (Raffles GEP, NUS Maths 1st Class Honours, NUS Deans List) and most importantly patient even with the most mathematically challenged.

So if you are in need of the solution to your mathematical woes, drop me a message!

Tutor: Mr Wu


Website: Singapore Maths Tuition | Patient and Dedicated Maths Tutor in Singapore