24 math riddles with answers, from easy to tricky
Twenty-four math riddles from our puzzle app, sorted from warm-up to properly hard. Answers are hidden, so you can actually try before you peek. Each one comes with a short explanation.
Here are 24 math riddles, from quick warm-ups to properly hard ones, each with an answer you can reveal. They come from our own puzzle game, Math Riddles & Logic Puzzles. We picked the ones that work as plain text (the app also has magic squares, kakuro grids and balance scales, which need a picture) and sorted them roughly from easy to hard.
Each answer is hidden. Tap “Answer” when you are ready. We would suggest giving each riddle at least a minute, because several of the easy-looking ones are traps.
Warm-up
1. The long multiplication
What is 5 × 10 × 1 × 2 × 3 × 5 × 0?
Answer
0. Look at the last number before you start multiplying. Anything times zero is zero, no matter what came before.
2. Half and add
Take half of 2, then add 2. What do you get?
Answer
3. Half of 2 is 1, and 1 + 2 = 3. It is easy to read it as “half of 2 + 2” and answer 2.
3. The apple basket
There are 10 apples in a basket. You take exactly 2. How many apples do you have?
Answer
2. The question asks how many you have, not how many are left in the basket.
4. The escaping sheep
A farmer keeps 17 sheep in a pen. One day, all but 9 escape through a hole in the fence. How many sheep are left in the pen?
Answer
9. “All but 9 escape” means 9 stayed. If you calculated 17 − 9 = 8, the wording got you.
5. The candy staircase
A staircase has 1, 2, 3, 4 and 5 candies on its steps, from bottom to top. You pick up every candy. How many do you have?
Answer
15. 1 + 2 + 3 + 4 + 5 = 15. Nothing hidden here. It is a warm-up for number 22.
Patterns and sequences
6. A famous sequence
1, 1, 2, 3, 5, 8, 13, ?
Answer
21. Each number is the sum of the two before it: 8 + 13 = 21. This is the Fibonacci sequence.
7. Only two divisors
2, 3, 5, 7, 11, ?
Answer
13. These are the prime numbers, numbers divisible only by 1 and themselves. The next one after 11 is 13.
8. The disguised squares
If 4 = 20, 5 = 30 and 6 = 42, then 7 = ?
Answer
56. Each number is multiplied by the next one up: 4 × 5 = 20, 5 × 6 = 30, 6 × 7 = 42. So 7 × 8 = 56.
9. The rotating number
1296, 6129, 9612, ?
Answer
2961. Each term moves the last digit to the front. Take the 2 from the end of 9612 and put it first.
10. The broken plus sign
If 2 + 3 = 10, 7 + 2 = 63 and 6 + 5 = 66, then 8 + 4 = ?
Answer
96. The ”+” hides a different rule: multiply the first number by the sum of both. 2 × 5 = 10, 7 × 9 = 63, 6 × 11 = 66, and 8 × 12 = 96.
11. Read it out loud
1, 11, 21, 1211, 111221, ?
Answer
312211. Each term describes the one before it. 1 is “one 1”, written 11. 11 is “two 1s”, written 21. 111221 is “three 1s, two 2s, one 1”, written 312211. It is called the look-and-say sequence, and it has nothing to do with arithmetic.
Word problems
12. Anna and Ben
Anna is twice as old as Ben. Together they are 24. How old is Anna?
Answer
16. If Ben is b, Anna is 2b, so 3b = 24 and Ben is 8. Anna is twice that.
13. Dividing by a half
Divide 30 by one half, then add 10. What is the result?
Answer
70. Dividing by ½ is the same as multiplying by 2, so 30 ÷ ½ = 60. Add 10 to get 70. “Divide by a half” and “divide in half” are different operations.
14. The bat and the ball
A bat and a ball cost $1.10 together. The bat costs $1 more than the ball. How many cents does the ball cost?
Answer
5 cents. Most people say 10, but then the bat would cost $1.10 and the total would be $1.20. With a 5 cent ball, the bat is $1.05 and together they make $1.10.
15. The fake banknote
A customer buys a $97 hat with a counterfeit $100 bill. The shopkeeper hands over the hat and $3 in real change. The bill turns out to be worthless. How much did the shopkeeper lose, in dollars?
Answer
100, if you value the hat at its $97 price. Count only what walked out of the shop: the hat and $3 in cash. (If you count what the hat cost the shop, the loss is smaller, but the riddle doesn’t give that number.) The fake bill never had any value, so it adds nothing to either side.
16. The frog in the well
A frog sits at the bottom of a 30-foot well. Each day it climbs 3 feet, and each night it slips back 2. On which day does it get out?
Answer
Day 28. The frog gains 1 foot per full day and night, so after 27 nights it is 27 feet up. On day 28 it climbs 3 feet, reaches the top and escapes before it can slip back. Answering 30 misses that last climb.
Order of operations
17. The one that starts arguments
What is 6 ÷ 2 × (1 + 2)?
Answer
9. Brackets first give 3. Division and multiplication have equal priority, so you go left to right: 6 ÷ 2 = 3, then 3 × 3 = 9. The common wrong answer, 1, comes from multiplying before dividing.
18. The fraction trap
What is 9 − 3 ÷ (1/3) + 1?
Answer
1. Dividing by a third means multiplying by 3, so 3 ÷ (1/3) = 9. That leaves 9 − 9 + 1 = 1.
19. Roman addition
What is XL + IX?
Answer
49. XL is 50 minus 10, so 40. IX is 10 minus 1, so 9. Together they make 49, which in Roman numerals is XLIX.
Tricky
20. Counting ones
A book has pages numbered from 1 to 200. How many times is the digit 1 printed?
Answer
140. Count each position separately. The ones place shows a 1 on 20 pages (1, 11, 21 and so on). The tens place shows a 1 on 20 pages (10 to 19 and 110 to 119). The hundreds place shows a 1 on all 100 pages from 100 to 199. 20 + 20 + 100 = 140.
21. Remainder one
A number leaves a remainder of 1 when divided by 2, 3, 4 or 5. It is also divisible by 7. What is the smallest such positive number?
Answer
301. One less than the number must divide evenly by 2, 3, 4 and 5, so it is a multiple of 60. Check 61, 121, 181, 241, 301. The first one divisible by 7 is 301, which is 7 × 43.
22. Gauss’s shortcut
What is the sum of all whole numbers from 1 to 100?
Answer
5050. Pair the ends: 1 + 100, 2 + 99, 3 + 98. Every pair adds to 101, and there are 50 pairs. 50 × 101 = 5050. The story goes that Carl Friedrich Gauss spotted this as a schoolboy.
23. TWO + TWO = FOUR
In the sum TWO + TWO = FOUR, each letter stands for a different digit. What digit is F?
Answer
1. Two three-digit numbers add up to less than 2000, so the fourth digit can only come from a carry, and a carry here is always 1. One working solution is 734 + 734 = 1468.
24. Sum of cubes
Find the smallest three-digit number above 300 that equals the sum of the cubes of its own digits.
Answer
370. 3³ + 7³ + 0³ = 27 + 343 + 0 = 370. Its neighbour 371 works too (27 + 343 + 1), but 370 comes first. Only four three-digit numbers have this property: 153, 370, 371 and 407.
How did you do?
If you got the bat and ball, the frog and the look-and-say sequence without peeking, nice work. Those three are easy to answer too quickly. Most of the traps here work the same way: a quick answer shows up before you have read the question properly, and it feels right.
If you want more, we post one puzzle a day on TikTok at @puzzle.a.day. The app has 120+ hand-built riddles across 26+ puzzle types, a daily puzzle, and a hint or a full step-by-step solution when you get stuck. It works offline. Get Math Riddles & Logic Puzzles for Android.
If you like other kinds of puzzles, we also make offline chess puzzles, a crossword app and a calm word search without a timer.