1 2 4 8 = 24: 14 solutions

Difficulty: EasyOpen in Solver

8 × (4 + 1 − 2) = 24

1 − 2 = -1
4 + -1 = 3
8 × 3 = 24

14 solutions

1 × 2 × (4 + 8) = 24Steps
1. 1 × 2 = 2
2. 4 + 8 = 12
3. 2 × 12 = 24
4 × (8 − 1 × 2) = 24Steps
1. 1 × 2 = 2
2. 8 − 2 = 6
3. 4 × 6 = 24
1 × 4 × (8 − 2) = 24Steps
1. 1 × 4 = 4
2. 8 − 2 = 6
3. 4 × 6 = 24
2 × (8 + 1 × 4) = 24Steps
1. 1 × 4 = 4
2. 8 + 4 = 12
3. 2 × 12 = 24
2 × (4 + 1 × 8) = 24Steps
1. 1 × 8 = 8
2. 4 + 8 = 12
3. 2 × 12 = 24
4 × (1 × 8 − 2) = 24Steps
1. 1 × 8 = 8
2. 8 − 2 = 6
3. 4 × 6 = 24
4 × (8 − 2 ÷ 1) = 24Steps
1. 2 ÷ 1 = 2
2. 8 − 2 = 6
3. 4 × 6 = 24
2 × (8 + 4 ÷ 1) = 24Steps
1. 4 ÷ 1 = 4
2. 8 + 4 = 12
3. 2 × 12 = 24
8 × (1 + 4 ÷ 2) = 24Steps
1. 4 ÷ 2 = 2
2. 1 + 2 = 3
3. 8 × 3 = 24
2 × (4 + 8 ÷ 1) = 24Steps
1. 8 ÷ 1 = 8
2. 4 + 8 = 12
3. 2 × 12 = 24
4 × (8 ÷ 1 − 2) = 24Steps
1. 8 ÷ 1 = 8
2. 8 − 2 = 6
3. 4 × 6 = 24
(4 + 8) ÷ (1 ÷ 2) = 24Steps
1. 4 + 8 = 12
2. 1 ÷ 2 = 1/2
3. 12 ÷ 1/2 = 24
(8 − 2) ÷ (1 ÷ 4) = 24Steps
1. 8 − 2 = 6
2. 1 ÷ 4 = 1/4
3. 6 ÷ 1/4 = 24

Solving hints

Build a factor pair: split the four numbers into two groups and try to make a factor pair of 24 — 3 × 8, 4 × 6, or 12 × 2 — then multiply the two groups.
No factor pair divides cleanly? Switch to sums: make two numbers add up to 24, or try shapes like (a ± b) × (c ± d) and (a + b + c) × d.

FAQ

Can 1 2 4 8 make 24?

Yes. Every one of them is listed above with step-by-step working.

How many solutions does 1 2 4 8 have?

14 — the list above is exhaustive, so every mathematically distinct way to combine the numbers is shown.

How difficult is 1 2 4 8?

It is rated “Easy” on our four-tier scale, based on whether whole-number intermediate steps suffice, how many distinct solutions exist, and whether the hand includes a two-digit card (10–13).