1 2 9 13 = 24: 14 solutions

Difficulty: HardOpen in Solver

1 × 2 + 9 + 13 = 24

1 × 2 = 2
9 + 13 = 22
2 + 22 = 24

14 solutions

1 × 9 + 2 + 13 = 24Steps
1. 1 × 9 = 9
2. 2 + 13 = 15
3. 9 + 15 = 24
1 × 13 + 2 + 9 = 24Steps
1. 1 × 13 = 13
2. 2 + 9 = 11
3. 13 + 11 = 24
2 ÷ 1 + 9 + 13 = 24Steps
1. 2 ÷ 1 = 2
2. 9 + 13 = 22
3. 2 + 22 = 24
2 + 9 + 13 ÷ 1 = 24Steps
1. 2 + 9 = 11
2. 13 ÷ 1 = 13
3. 11 + 13 = 24
2 + 13 + 9 ÷ 1 = 24Steps
1. 2 + 13 = 15
2. 9 ÷ 1 = 9
3. 15 + 9 = 24
13 + 1 × (2 + 9) = 24Steps
1. 2 + 9 = 11
2. 1 × 11 = 11
3. 13 + 11 = 24
1 × (13 + 2 + 9) = 24Steps
1. 2 + 9 = 11
2. 13 + 11 = 24
3. 1 × 24 = 24
(13 + 2 + 9) ÷ 1 = 24Steps
1. 2 + 9 = 11
2. 13 + 11 = 24
3. 24 ÷ 1 = 24
13 + (2 + 9) ÷ 1 = 24Steps
1. 2 + 9 = 11
2. 11 ÷ 1 = 11
3. 13 + 11 = 24
9 + 1 × (2 + 13) = 24Steps
1. 2 + 13 = 15
2. 1 × 15 = 15
3. 9 + 15 = 24
9 + (2 + 13) ÷ 1 = 24Steps
1. 2 + 13 = 15
2. 15 ÷ 1 = 15
3. 9 + 15 = 24
2 + 1 × (9 + 13) = 24Steps
1. 9 + 13 = 22
2. 1 × 22 = 22
3. 2 + 22 = 24
2 + (9 + 13) ÷ 1 = 24Steps
1. 9 + 13 = 22
2. 22 ÷ 1 = 22
3. 2 + 22 = 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 9 13 make 24?

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

How many solutions does 1 2 9 13 have?

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

How difficult is 1 2 9 13?

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).