Homeschool Maths Puzzles with Answers: The “Average” Question

The average of 5 numbers is 73. When 2 numbers were removed, the average decreased by 3. What is the average of the 2 numbers that were removed?


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.

Answer:

This is literally an “average” question. 😛 The word “average” appears 3 times.

The trick is to focus on the total instead.

The total of the 5 numbers is: 73×5=365.

After removing 2 numbers, the average is 73-3=70.

Hence, the total of the 3 remaining numbers is: 70×3=210.

We can then conclude that, the total of the 2 removed numbers is:

365-210=155.

Hence, the average of the 2 removed numbers is: 155/2=77.5 or 75 1/2.

Slow and Steady Snail (Homeschool Math Favorite Challenging Puzzles)

This is a favorite type of homeschool math challenging puzzle — The Snail question.

Question: An aquarium is 47 cm deep. A snail starts at the bottom of the aquarium. Each day, during the daytime the snail climbs up 8 cm, and during the nighttime the snail slides down 3 cm. How many days will it take for the snail to climb out of the aquarium?


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.

Solution:

A tempting answer would be 10 days. This is a trick! Those who get the answer “10 days” reason like this: each day the snail moves a net distance of 8-3=5 cm.

Hence, 47/5=9 R 2.

At the end of the 9th day, the snail moved 45 cm. Thus, rounding up will give 10 days as the answer. However, there is a tricky part to the question!

The correct answer is 9 days.

We can do a list:

Day 1 — 5 cm

Day 2 — 10 cm

Day 3 — 15 cm

Day 8 — 40 cm

Day 9 day time — 40 +8 = 48cm > 47 cm !!!

The snail is already out of the aquarium on Day 9!

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.

Solution

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

Hence,

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

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.

Solution

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.

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:

50-12-6=32

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

D=10

Answer: Dennis has 10 stickers.

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.

Solution:

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

 

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: https://mathtuition88.com/category/homeschool-math-challenging-puzzles/