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1 2 5 7 = 24: 8 solutions

Difficulty: EasyOpen in Solver

1 × 2 × (5 + 7) = 24

  1. 1 × 2 = 2
  2. 5 + 7 = 12
  3. 2 × 12 = 24

8 solutions

  • 2 × (7 + 1 × 5) = 24Steps
    1. 1 × 5 = 5
    2. 7 + 5 = 12
    3. 2 × 12 = 24
  • 2 × (5 + 1 × 7) = 24Steps
    1. 1 × 7 = 7
    2. 5 + 7 = 12
    3. 2 × 12 = 24
  • 2 × (7 + 5 ÷ 1) = 24Steps
    1. 5 ÷ 1 = 5
    2. 7 + 5 = 12
    3. 2 × 12 = 24
  • 2 × (5 + 7 ÷ 1) = 24Steps
    1. 7 ÷ 1 = 7
    2. 5 + 7 = 12
    3. 2 × 12 = 24
  • 5 × (7 − 2) − 1 = 24Steps
    1. 7 − 2 = 5
    2. 5 × 5 = 25
    3. 25 − 1 = 24
  • (5 + 7) ÷ (1 ÷ 2) = 24Steps
    1. 5 + 7 = 12
    2. 1 ÷ 2 = 1/2
    3. 12 ÷ 1/2 = 24
  • (1 + 7) × (5 − 2) = 24Steps
    1. 1 + 7 = 8
    2. 5 − 2 = 3
    3. 8 × 3 = 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.

Related hands

FAQ

Can 1 2 5 7 make 24?

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

How many solutions does 1 2 5 7 have?

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

How difficult is 1 2 5 7?

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).