1 6 8 12 = 24: 13 solutions

Difficulty: HardOpen in Solver

12 × (8 − 1 × 6) = 24

1 × 6 = 6
8 − 6 = 2
12 × 2 = 24

13 solutions

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

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

How many solutions does 1 6 8 12 have?

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

How difficult is 1 6 8 12?

It is rated “Hard” 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).