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1 1 3 7 = 24: 7 solutions

Difficulty: EasyOpen in Solver

3 × (7 + 1 × 1) = 24

  1. 1 × 1 = 1
  2. 7 + 1 = 8
  3. 3 × 8 = 24

7 solutions

  • 3 × (7 + 1 ÷ 1) = 24Steps
    1. 1 ÷ 1 = 1
    2. 7 + 1 = 8
    3. 3 × 8 = 24
  • 1 × 3 × (1 + 7) = 24Steps
    1. 1 × 3 = 3
    2. 1 + 7 = 8
    3. 3 × 8 = 24
  • 3 × (1 + 1 × 7) = 24Steps
    1. 1 × 7 = 7
    2. 1 + 7 = 8
    3. 3 × 8 = 24
  • 3 × (1 + 7 ÷ 1) = 24Steps
    1. 7 ÷ 1 = 7
    2. 1 + 7 = 8
    3. 3 × 8 = 24
  • (1 + 3) × (7 − 1) = 24Steps
    1. 1 + 3 = 4
    2. 7 − 1 = 6
    3. 4 × 6 = 24
  • (1 + 7) ÷ (1 ÷ 3) = 24Steps
    1. 1 + 7 = 8
    2. 1 ÷ 3 = 1/3
    3. 8 ÷ 1/3 = 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 1 3 7 make 24?

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

How many solutions does 1 1 3 7 have?

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

How difficult is 1 1 3 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).