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1 5 7 11 = 24: 9 solutions

Difficulty: HardOpen in Solver

1 + 5 + 7 + 11 = 24

  1. 1 + 5 = 6
  2. 7 + 11 = 18
  3. 6 + 18 = 24

9 solutions

  • 7 × 1 × 5 − 11 = 24Steps
    1. 1 × 5 = 5
    2. 7 × 5 = 35
    3. 35 − 11 = 24
  • 5 × 7 − 1 × 11 = 24Steps
    1. 5 × 7 = 35
    2. 1 × 11 = 11
    3. 35 − 11 = 24
  • 5 × 7 − 11 ÷ 1 = 24Steps
    1. 5 × 7 = 35
    2. 11 ÷ 1 = 11
    3. 35 − 11 = 24
  • 7 ÷ (1 ÷ 5) − 11 = 24Steps
    1. 1 ÷ 5 = 1/5
    2. 7 ÷ 1/5 = 35
    3. 35 − 11 = 24
  • 1 × (5 × 7 − 11) = 24Steps
    1. 5 × 7 = 35
    2. 35 − 11 = 24
    3. 1 × 24 = 24
  • (5 × 7 − 11) ÷ 1 = 24Steps
    1. 5 × 7 = 35
    2. 35 − 11 = 24
    3. 24 ÷ 1 = 24
  • (1 + 5) × (11 − 7) = 24Steps
    1. 1 + 5 = 6
    2. 11 − 7 = 4
    3. 6 × 4 = 24
  • (1 + 11) × (7 − 5) = 24Steps
    1. 1 + 11 = 12
    2. 7 − 5 = 2
    3. 12 × 2 = 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 5 7 11 make 24?

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

How many solutions does 1 5 7 11 have?

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

How difficult is 1 5 7 11?

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).