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1 7 7 10 = 24: 11 solutions

Difficulty: HardOpen in Solver

1 × 7 + 7 + 10 = 24

  1. 1 × 7 = 7
  2. 7 + 10 = 17
  3. 7 + 17 = 24

11 solutions

  • 1 × 10 + 7 + 7 = 24Steps
    1. 1 × 10 = 10
    2. 7 + 7 = 14
    3. 10 + 14 = 24
  • 7 ÷ 1 + 7 + 10 = 24Steps
    1. 7 ÷ 1 = 7
    2. 7 + 10 = 17
    3. 7 + 17 = 24
  • 7 + 7 + 10 ÷ 1 = 24Steps
    1. 7 + 7 = 14
    2. 10 ÷ 1 = 10
    3. 14 + 10 = 24
  • 10 + 1 × (7 + 7) = 24Steps
    1. 7 + 7 = 14
    2. 1 × 14 = 14
    3. 10 + 14 = 24
  • 1 × (10 + 7 + 7) = 24Steps
    1. 7 + 7 = 14
    2. 10 + 14 = 24
    3. 1 × 24 = 24
  • (10 + 7 + 7) ÷ 1 = 24Steps
    1. 7 + 7 = 14
    2. 10 + 14 = 24
    3. 24 ÷ 1 = 24
  • 10 + (7 + 7) ÷ 1 = 24Steps
    1. 7 + 7 = 14
    2. 14 ÷ 1 = 14
    3. 10 + 14 = 24
  • 7 + 1 × (7 + 10) = 24Steps
    1. 7 + 10 = 17
    2. 1 × 17 = 17
    3. 7 + 17 = 24
  • 7 + (7 + 10) ÷ 1 = 24Steps
    1. 7 + 10 = 17
    2. 17 ÷ 1 = 17
    3. 7 + 17 = 24
  • (1 + 7) × (10 − 7) = 24Steps
    1. 1 + 7 = 8
    2. 10 − 7 = 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 7 7 10 make 24?

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

How many solutions does 1 7 7 10 have?

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

How difficult is 1 7 7 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).