Maths tricks · trick 10 of 25 · free

Digit-sum magic — Maths trick for kids

The digits of every number in the 9 times table add up to a number in the 9 table: 72 → 7 + 2 = 9, 315 → 3 + 1 + 5 = 9, 7623 → 18. A magician uses this to find a digit a friend has hidden.

The trick

Digits add to the 9 table — “the digits of any 9-table number add up to 9, 18, 27 …”

  1. Add the digits you can see.
  2. Find the next number in the 9 table (9, 18, 27 …) above that total.
  3. The hidden digit is the difference. (Any number minus its digit sum is in the 9 table too.)

Use it for: Mind-reading tricks, checking answers in the 9 table, and divisibility by 9.

Worked example: 3?5 is in the 9 times table. One digit is hidden, and it is not 0. What is the hidden digit? → 1

  1. Add the digits you see: 3 + 5 = 8.
  2. The next number in the 9 table is 9.
  3. 9 − 8 = 1, so the number is 315.

Check: 315 ÷ 9 = 35 ✓

✏️ Practice

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🏁 Trick 10 test

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🖨️ Digit Sum Magic Worksheet

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