Math Brain Teasers: 25 Puzzles with Step-by-Step Answers on Riddlepedia
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Math Brain Teasers: 25 Puzzles with Step-by-Step Answers

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A math brain teaser isn’t a worksheet in disguise. The numbers are usually small, and the hard part is spotting what the question is really asking: a fence-post count, a sneaky “half,” or a pattern that grows faster than you expect. Once you see it, the math itself takes seconds.

These 25 math brain teasers start with puzzles a 9-year-old can solve in their head and build up to classics that stump plenty of adults. Every answer shows the working step by step, so you can check it, teach it, or argue about it. Grab a pencil for the tricky section.

Easy Math Brain Teasers

A farmer has some chickens and some cows. Together they have 10 heads and 28 legs. How many cows are there?

Hint
Pretend every animal is a chicken first. How many legs are missing?
Answer
4 cows. If all 10 animals were chickens, there’d be 20 legs. The extra 8 legs come from cows, and each cow adds 2 extra legs, so there are 8 ÷ 2 = 4 cows (and 6 chickens). Check it: 4 × 4 + 6 × 2 = 28.

A brick weighs 1 kilogram plus half a brick. How much does a whole brick weigh?

Hint
If 1 kilogram is one half of the brick, what’s the other half?
Answer
2 kilograms. The brick is “1 kg + half a brick,” so the 1 kg must be the other half. Two halves of 1 kg make 2 kg.

You have a ribbon 12 meters long. How many cuts do you need to make to get 12 pieces, each 1 meter long?

Hint
Try it with a short ribbon first: how many cuts make 2 pieces?
Answer
11 cuts. Each cut adds one piece. You start with 1 piece, so you need 11 cuts to reach 12.

Three numbers in a row (like 4, 5, 6) add up to 72. What are they?

Hint
The middle number is the average.
Answer
23, 24 and 25. 72 ÷ 3 = 24 is the middle number, and 23 + 24 + 25 = 72.

A pen costs twice as much as a pencil. Together they cost 90 cents. How much does the pencil cost?

Hint
Think of the pencil as 1 share and the pen as 2 shares.
Answer
30 cents. Pencil plus pen is 3 shares, and 90 ÷ 3 = 30. The pen costs 60 cents.

A patch of moss doubles in size every day. On day 20 it covers a whole rock. On which day did it cover exactly half the rock?

Hint
Go backward one day from the full rock.
Answer
Day 19. Because it doubles every day, it was half the size one day before it covered the whole rock.

Using exactly eight 8s and only addition, can you make 1000?

Hint
Start with the biggest number you can build from three 8s.
Answer
888 + 88 + 8 + 8 + 8 = 1000. That’s 3 + 2 + 1 + 1 + 1 = 8 eights, and 888 + 88 = 976, plus 24 is 1000.

Sara is 6 and her mom is 30. In how many years will her mom be exactly 3 times as old as Sara?

Hint
Add the same number of years to both ages and test.
Answer
6 years. Sara will be 12 and her mom 36, and 36 = 3 × 12. (Mom is always 24 years older, and 24 is twice Sara’s age only when Sara is 12.)

Medium Math Brain Teasers

If 3 cats catch 3 mice in 3 minutes, how many cats are needed to catch 100 mice in 100 minutes?

Hint
How long does it take one cat to catch one mouse?
Answer
3 cats. Each cat catches 1 mouse every 3 minutes. In 100 minutes, 3 cats each catch 33⅓ mice, and 3 × 33⅓ = 100.

What’s the largest number of pieces you can cut a round pizza into with 3 straight cuts? (You can’t move the pieces between cuts.)

Hint
Six is not the most. Make every new cut cross all the cuts before it.
Answer
7 pieces. The first cut makes 2 pieces, the second (crossing the first) makes 4, and the third, crossing both earlier cuts at different points, passes through 3 pieces and splits each one, making 7.

A shirt is 50% off. At the checkout you get another 50% off the sale price. Is the shirt free?

Hint
Try it with a $20 shirt.
Answer
No, you pay 25% of the original price. A $20 shirt drops to $10, and half of $10 is $5, which is a quarter of $20.

What’s the smallest whole number bigger than 1 that leaves a remainder of 1 when you divide it by 2, 3, 4, 5 or 6?

Hint
Find the smallest number that 2, 3, 4, 5 and 6 all divide into evenly, then add 1.
Answer
  1. The smallest number divisible by 2, 3, 4, 5 and 6 is 60, so 61 leaves a remainder of 1 every time.

How many two-digit numbers have digits that add up to 9?

Hint
The tens digit can be anything from 1 to 9. What does each one force the ones digit to be?
Answer
  1. They are 18, 27, 36, 45, 54, 63, 72, 81 and 90.

You place the numbers 1 to 9 in a 3 × 3 grid so that every row, every column and both diagonals add up to the same total. What is that total?

Hint
Add up 1 through 9, then share it among the three rows.
Answer
  1. 1 + 2 + … + 9 = 45, and the three rows share it equally, so each row is 45 ÷ 3 = 15.

On day 1 you get 1 cent. Every day after that, you get double what you got the day before. On which day do you first get more than $10 in a single day?

Hint
Keep doubling: 1, 2, 4, 8, 16…
Answer
Day 11. The amounts go 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 cents on days 1 to 10, and 1,024 cents ($10.24) on day 11.

You drive 60 km to Grandma’s at 30 km/h and drive the same 60 km home at 60 km/h. What is your average speed for the whole trip?

Hint
It isn’t 45. Work out the total time.
Answer
40 km/h. The trip there takes 2 hours and the trip home takes 1 hour, so you cover 120 km in 3 hours, and 120 ÷ 3 = 40.

A 3 × 3 × 3 cube is painted red on the outside and then cut into 27 small cubes. How many small cubes have red paint on exactly two faces?

Hint
Cubes with two painted faces sit along the edges, but not at the corners.
Answer
  1. A cube has 12 edges, and each edge has exactly 1 small cube that isn’t a corner. (8 corner cubes have 3 painted faces, 6 face-center cubes have 1, and the 1 in the very middle has none.)

Tricky Math Brain Teasers for Grown-Ups

Two trains start 120 km apart and head toward each other, one at 40 km/h and the other at 20 km/h. A bird starts at the front of one train and flies at 75 km/h back and forth between them until they meet. How far does the bird fly?

Hint
Don’t follow the bird. Work out how long it flies.
Answer
150 kilometers. The trains close the gap at 40 + 20 = 60 km/h, so they meet after 120 ÷ 60 = 2 hours. The bird flies the whole time, and 75 × 2 = 150.

The hands of a clock show exactly 3:15. What is the angle between the hour hand and the minute hand?

Hint
The hour hand isn’t pointing exactly at the 3.
Answer
7.5 degrees. The minute hand points at the 3, which is 90° from the top. The hour hand has moved a quarter of the way from the 3 to the 4, and that gap is 30°, so it’s 7.5° past the minute hand.

Three friends pay $30 for a hotel room, $10 each. The clerk realizes the room costs only $25 and sends the bellhop back with $5. The bellhop keeps $2 and gives each friend $1. Now each friend has paid $9, and 3 × $9 = $27. Add the bellhop’s $2 and you get $29. Where did the missing dollar go?

Hint
Should the $2 be added to the $27, or is it already inside it?
Answer
There is no missing dollar. The friends paid $27 in total: $25 for the room plus $2 for the bellhop. Adding the $2 again counts it twice. The right sum is $27 paid + $3 returned = $30.

You have a 3-liter jug and a 5-liter jug, both with no markings, and a tap. How can you measure exactly 4 liters?

Hint
Fill the big jug and use the small one to take some away.
Answer
Fill the big jug twice. Fill the 5-liter jug and pour it into the 3-liter jug, leaving 2 liters in the big one. Empty the 3-liter jug and pour the 2 liters into it. Fill the 5-liter jug again, then top up the 3-liter jug, which takes just 1 liter. Exactly 4 liters are left in the 5-liter jug.

A census taker asks a woman the ages of her three daughters. She says, “The product of their ages is 36.” He says that isn’t enough. She says, “The sum of their ages is our house number.” He looks at the house number and still can’t tell. She adds, “My oldest daughter, who is older than both her sisters, loves chess.” How old are the daughters?

Hint
List every set of three whole-number ages that multiply to 36, add each set up, and look for a sum that appears twice.
Answer
2, 2 and 9. The sets that multiply to 36 add up to 38, 21, 16, 14, 13, 13, 11 and 10. Only 13 appears twice (1, 6, 6 and 2, 2, 9), which is why the house number didn’t help. Only 2, 2, 9 has one daughter older than both others.

You climb a staircase of 5 steps, taking either 1 or 2 steps at a time. How many different ways can you climb it?

Hint
Count the ways for 1, 2 and 3 steps and look for a pattern.
Answer
8 ways. 1 step has 1 way, 2 steps have 2, and after that each number of steps is the sum of the two before it (your last move was a 1 or a 2): 3, 5, then 8.

In a family, the product of two sisters’ ages is 48 and one is 2 years older than the other. How old is each sister?

Hint
Look for two numbers 2 apart that multiply to 48.
Answer
6 and 8. 6 × 8 = 48, and 8 − 6 = 2. Other factor pairs of 48 (1 × 48, 2 × 24, 3 × 16, 4 × 12) are too far apart.

Your first four test scores average 80. What score do you need on the fifth test to raise your average to exactly 82?

Hint
Work with total points, not averages.
Answer
  1. Four tests at an average of 80 make 320 points. An average of 82 over five tests needs 5 × 82 = 410 points, and 410 − 320 = 90.

How to Use These Math Brain Teasers

  • Teaser of the day: in class, post one teaser on the board in the morning and let students submit answers with their working on a sticky note. Read out the best explanation, not just the first right answer.
  • Estimate first: before solving, everyone writes a gut-feeling answer. Comparing gut answers with real ones (average speed, the discount, the pizza) is the most memorable part of the lesson.
  • Family dinner challenge: one person reads a teaser, and nobody can use a calculator or phone. Kids take the easy round and adults the tricky one, then swap.
  • Change the numbers: once a puzzle is solved, change one number (a 4-liter jug, a 6-step staircase) and solve the new version. It’s the best way to check the method really makes sense.

For more number fun, try our number riddles, our logic riddles or these calculator riddles.