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🎩 10 maths magic tricks

10 maths magic tricks, and the secret behind each one

These tricks always work, because maths always works. Learn the steps, perform them for friends and then read the secret to see why.

Updated 21 October 2026. Every answer on this page is checked.

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How to play

  • Practise the trick once on your own before performing.
  • Never reveal the secret until after the trick. Magicians never do.
  • Ask your audience to use a calculator or paper to make it feel fair.

The always-five number

  1. Ask a friend to think of any number.
  2. Double it.
  3. Add 10.
  4. Halve the result.
  5. Subtract the number they first thought of.

The answer is always 5.

Why it works: If the number is x: double it to get 2x, add 10 to get 2x + 10, halve to get x + 5, and subtract x to leave 5. The first number cancels out.

Multiply any two-digit number by 11

  1. Take the two digits of the number, for example 36.
  2. Write the first digit, then the sum of the two digits, then the last digit: 3, (3 + 6), 6.
  3. That makes 396, so 36 × 11 = 396.
  4. If the sum is 10 or more, carry the 1: 78 × 11 gives 7, (7 + 8 = 15), 8, so 7 + 1, 5, 8 = 858.

36 × 11 = 396 and 78 × 11 = 858.

Why it works: Multiplying by 11 is the same as multiplying by 10 and adding the number once more, which adds the digits in the middle.

The 9 times table on your fingers

  1. Hold up both hands with all ten fingers.
  2. To find 9 × 4, fold down your fourth finger from the left.
  3. Count the fingers to the left of the folded finger: 3. That is the tens.
  4. Count the fingers to the right: 6. That is the ones.

9 × 4 = 36. It works for 9 × 1 up to 9 × 10.

Why it works: Folding finger n leaves n − 1 fingers on the left and 10 − n on the right, and (n − 1) tens plus (10 − n) ones equals 9n.

Square a number ending in 5

  1. Take a number ending in 5, for example 35.
  2. Take the digits before the 5: 3.
  3. Multiply that by the next number up: 3 × 4 = 12.
  4. Write 25 after it.

35² = 1225. Try 65² = 4225 and 85² = 7225.

Why it works: A number (10a + 5) squared is 100a(a + 1) + 25, which gives a(a + 1) followed by 25.

Guess the birthday

  1. Ask a friend for the month of their birthday as a number, for example July = 7.
  2. Multiply by 5, then add 6, then multiply by 4, then add 9, then multiply by 5.
  3. Add the day of the month, for example 15.
  4. Ask for the total and subtract 165.

The answer is the month and day together: 715 means 7 and 15, so 15 July.

Why it works: The month m becomes 100m + 165 after all the steps. Adding the day d and subtracting 165 leaves 100m + d.

The 1089 trick

  1. Pick a three-digit number whose first and last digits differ by at least 2, for example 832.
  2. Reverse it: 238.
  3. Subtract the smaller from the larger: 832 − 238 = 594.
  4. Reverse that: 495.
  5. Add: 594 + 495.

The answer is always 1089.

Why it works: After subtracting, the middle digit is always 9 and the outer digits add up to 9, so the number and its reverse always add to 1089.

Add ten numbers in a flash

  1. Ask a friend to write any two numbers, for example 3 and 5.
  2. Each new number is the sum of the previous two: 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.
  3. While they add them up, look at the seventh number: 55.
  4. Multiply it by 11.

The sum is 55 × 11 = 605.

Why it works: In any sequence built this way, the sum of the first ten terms is exactly 11 times the seventh term.

The magic of 9

  1. Take any number from the 9 times table up to 90, such as 63.
  2. Add its digits: 6 + 3 = 9.
  3. Try 72: 7 + 2 = 9. Try 45: 4 + 5 = 9.

The digits of multiples of 9 (up to 90) always add to 9.

Why it works: Numbers 10a + b that are multiples of 9 have a + b divisible by 9, and for two-digit multiples the sum is exactly 9.

The 142857 circle

  1. Write 142857.
  2. Multiply it by 2: 285714.
  3. Multiply by 3: 428571, by 4: 571428, by 5: 714285, by 6: 857142.

Each answer uses the same six digits in the same circular order.

Why it works: 142857 is one-seventh written as a repeating decimal, so multiples of it from 1 to 6 give the same repeating pattern started at a different place.

The calendar square

  1. Look at any month on a calendar.
  2. Draw a square around any 3 by 3 block of dates.
  3. Add up the nine dates.
  4. Multiply the middle date by 9.

The two answers are always the same.

Why it works: The dates pair up around the middle date (for example, one before and one after add to double the middle), so the nine numbers always add to nine times the middle.

FAQ

Maths magic tricks: questions people ask

Are these tricks really always true?

Yes. Each one is a mathematical fact, and the explanation shows why.

What age are they for?

Ages 8 to 14. The explanations use simple algebra that older children will enjoy.

Can we use a calculator?

Yes, it makes the trick look more impressive.

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