How to make 24: tricks that crack almost every deal

Strong players don’t try combinations at random. They aim for a handful of targets and work backwards.

1. Aim for a factor pair

24 = 1 × 24 = 2 × 12 = 3 × 8 = 4 × 6. Most solutions build one number of a pair from two cards and the other number from the remaining two. For 1, 5, 7, 3: 1 + 5 = 6 and 7 − 3 = 4, so 6 × 4 = 24. If one pair doesn’t work, move on to the next.

2. Work backwards from the last step

Ask what the last operation could be. If three cards can make 16, the fourth needs to be 8 (16 + 8). If three cards can make 3, the fourth needs to be 8 (3 × 8). For 2, 4, 6, 8: can 2, 4 and 6 make 16? Yes – 4 × (6 − 2) = 16 – so 4 × (6 − 2) + 8 = 24. Checking “what do the other three need to make?” for each card turns guessing into a short checklist.

3. The 0-and-1 trick

If two cards are equal, their difference is 0 and their quotient is 1. Adding 0 or multiplying by 1 removes a pair without changing the result. With 3, 8, 5, 5: 3 × 8 × (5 ÷ 5) = 24.

4. Don’t forget fractions

The hardest deals need a fraction in the middle:

• 3, 3, 8, 8 → 8 ÷ (3 − 8 ÷ 3) = 8 ÷ (1/3) = 24
• 1, 5, 5, 5 → 5 × (5 − 1 ÷ 5) = 5 × 24/5 = 24
• 1, 3, 4, 6 → 6 ÷ (1 − 3 ÷ 4) = 6 ÷ 1/4 = 24

When nothing else works, look for a way to make a fraction like 1/3 or 1/4 and divide by it.

5. Common shapes worth memorising

• a × b − c × d: 5, 6, 2, 3 → 5 × 6 − 2 × 3 = 24
• (a + b) × (c − d): 1, 5, 7, 3 → (1 + 5) × (7 − 3) = 24
• (a − b ÷ c) × d: see 1, 5, 5, 5 above

Practise in Make 24 – every deal there is solvable, and “Show answer” reveals one route when you’re stuck.