Reference

Make 24: Worked Examples

Verified solutions for famous number sets — including the classic 3, 8, 3, 8 puzzle searched worldwide.

Updated June 2026

Solutions

Classic puzzles solved

Each solution uses all four numbers exactly once. New to the rules? How to play the 24 game.

Classic

3 · 8 · 3 · 8

8 ÷ (3 − 8 ÷ 3) = 24

Step by step: 8 ÷ 3 = 8/3, then 3 − 8/3 = 1/3, then 8 ÷ (1/3) = 24.

Hard

1 · 5 · 5 · 5

(5 − 1 ÷ 5) × 5 = 24

Uses division to create a fraction (24/5) before multiplying back to 24.

Easy

4 · 6 · 2 · 6

(6 + 6) × (4 − 2) = 24

Beginner-friendly — teaches factor pairs (12 × 2).

Medium

2 · 3 · 4 · 5

(5 + 3) × (4 − 2 ÷ 2) = 24

Uses 2 ÷ 2 = 1 so that 4 − 1 = 3, then 8 × 3 = 24.

Easy

6 · 6 · 6 · 6

6 + 6 + 6 + 6 = 24

When all four numbers are 6, pure addition works.

Hard

1 · 3 · 4 · 6

6 ÷ (1 − 3 ÷ 4) = 24

Similar to 3-8-3-8: parentheses create 1/4, then 6 ÷ (1/4) = 24.

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