1 5 9 10 = 24: 14 solutions

Difficulty: HardOpen in Solver

1 × 5 + 9 + 10 = 24

1 × 5 = 5
9 + 10 = 19
5 + 19 = 24

14 solutions

1 × 9 + 5 + 10 = 24Steps
1. 1 × 9 = 9
2. 5 + 10 = 15
3. 9 + 15 = 24
1 × 10 + 5 + 9 = 24Steps
1. 1 × 10 = 10
2. 5 + 9 = 14
3. 10 + 14 = 24
5 ÷ 1 + 9 + 10 = 24Steps
1. 5 ÷ 1 = 5
2. 9 + 10 = 19
3. 5 + 19 = 24
5 + 9 + 10 ÷ 1 = 24Steps
1. 5 + 9 = 14
2. 10 ÷ 1 = 10
3. 14 + 10 = 24
5 + 10 + 9 ÷ 1 = 24Steps
1. 5 + 10 = 15
2. 9 ÷ 1 = 9
3. 15 + 9 = 24
10 + 1 × (5 + 9) = 24Steps
1. 5 + 9 = 14
2. 1 × 14 = 14
3. 10 + 14 = 24
1 × (10 + 5 + 9) = 24Steps
1. 5 + 9 = 14
2. 10 + 14 = 24
3. 1 × 24 = 24
(10 + 5 + 9) ÷ 1 = 24Steps
1. 5 + 9 = 14
2. 10 + 14 = 24
3. 24 ÷ 1 = 24
10 + (5 + 9) ÷ 1 = 24Steps
1. 5 + 9 = 14
2. 14 ÷ 1 = 14
3. 10 + 14 = 24
9 + 1 × (5 + 10) = 24Steps
1. 5 + 10 = 15
2. 1 × 15 = 15
3. 9 + 15 = 24
9 + (5 + 10) ÷ 1 = 24Steps
1. 5 + 10 = 15
2. 15 ÷ 1 = 15
3. 9 + 15 = 24
5 + 1 × (9 + 10) = 24Steps
1. 9 + 10 = 19
2. 1 × 19 = 19
3. 5 + 19 = 24
5 + (9 + 10) ÷ 1 = 24Steps
1. 9 + 10 = 19
2. 19 ÷ 1 = 19
3. 5 + 19 = 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 5 9 10 make 24?

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

How many solutions does 1 5 9 10 have?

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

How difficult is 1 5 9 10?

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).