Math Brain Teasers (With Answers)
Free math brain teasers with fully worked answers — number puzzles, age problems and logic traps — plus an interactive player. Reason it out, then check the working.
Math brain teasers that reward clever thinking over heavy calculation — number puzzles, age problems and logic traps, each with the full working. Use the player for one at a time, or scroll down for the whole list. Watch out for the "trap" answers that come from rushing.
All math brain teasers (with worked answers)
I am an odd number. Take away one letter and I become even. Which number am I?
Hint
Think about the word, not the value.
Answer
Seven — remove the "s" and you get "even".
Using only addition, how can you add eight 8s to make 1,000?
Hint
You don't need eight separate 8s as units.
Answer
888 + 88 + 8 + 8 + 8 = 1,000.
A farmer has 17 sheep. All but 9 run away. How many are left?
Hint
Read "all but nine" carefully.
Answer
9 — "all but 9 run away" means 9 remain.
How many times can you subtract 5 from 25?
Hint
After the first subtraction it is no longer 25.
Answer
Once — after that you are subtracting from 20.
A book costs $5 plus half its own price. How much does it cost?
Hint
Let the price be x and write an equation.
Answer
$10. If x = 5 + x/2, then x/2 = 5, so x = 10.
A snail climbs a 10-metre well, going up 3 m each day and slipping back 2 m each night. How many days to escape?
Hint
On the last day it climbs out before slipping.
Answer
8 days. It nets 1 m a day, but on day 8 it starts at 7 m and climbs 3 m to escape.
A clock takes 6 seconds to strike 4 o'clock. How long does it take to strike 12?
Hint
Count the gaps between strikes, not the strikes.
Answer
22 seconds. Four strikes have 3 gaps (6 s ÷ 3 = 2 s each); twelve strikes have 11 gaps × 2 s = 22 s.
A man is 4 times as old as his son. In 20 years he will be twice as old. How old is the son now?
Hint
Set up two ages and an equation.
Answer
10. If the son is s, the father is 4s; 4s + 20 = 2(s + 20) gives s = 10.
In a room, 100 people wear hats and 1 person does not (so 99% wear hats). How many hat-wearers must leave so that 98% of those remaining wear hats?
Hint
The 1 person without a hat stays; solve for the rest.
Answer
50. After x leave: (99 − x)/(100 − x) = 0.98 gives x = 50.
Divide 30 by a half and then add 10. What do you get?
Hint
Dividing by a half is the same as multiplying by 2.
Answer
70. 30 ÷ 0.5 = 60, then 60 + 10 = 70.
What three different positive whole numbers give the same result whether you add them or multiply them?
Hint
Start small.
Answer
1, 2 and 3 — they add to 6 and multiply to 6.
If a hen and a half lay an egg and a half in a day and a half, how many eggs does one hen lay in one day?
Hint
Work out the rate per hen per day.
Answer
Two-thirds of an egg. 1.5 hens lay 1 egg in 1.5 days, so 1 hen lays 1 egg in 1.5 days — that is 2/3 of an egg per day.
I am a three-digit number. My tens digit is five more than my ones digit, and my hundreds digit is eight less than my tens digit. What number am I?
Hint
Try writing the digits in terms of the ones digit.
Answer
194. Ones = 4, tens = 9 (4 + 5), hundreds = 1 (9 − 8).
If you multiply together every number shown on a phone's keypad (0 to 9), what is the product?
Hint
One of those digits is special.
Answer
Zero — multiplying by 0 makes the whole product 0.
Two is company and three is a crowd. What are four and five?
Hint
It is an arithmetic joke.
Answer
Nine (4 + 5 = 9).
A bag holds red and blue balls. You pick in the dark. How many must you take to be sure of a matching pair, if there are only two colours?
Hint
Think about the worst case.
Answer
Three — with only two colours, three balls guarantee at least two of one colour.
From teasers to tests
Many of these reward the same care that real aptitude tests demand: read closely, don't rush, and check the obvious answer. When you're ready to measure that skill, try the numerical reasoning test and the logical reasoning test. For lighter fare, see our funny brain teasers.
Frequently asked questions
What are math brain teasers?
Math brain teasers are puzzles that use numbers or logic but reward clever thinking over heavy calculation — like "How many times can you subtract 5 from 25?" (once). Each one here comes with the full working.
Are math brain teasers good for the brain?
They sharpen number sense and careful reading. Many have a "trap" answer that comes from rushing, so they train you to slow down and check — a habit that helps on real tests too.
Are these suitable for kids and adults?
Yes. The easier ones suit upper-primary children; several will challenge adults. Try the answer before revealing the working.