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1 11 12 13 = 24: 5 solutions

Difficulty: HardOpen in Solver

12 × (13 − 1 × 11) = 24

  1. 1 × 11 = 11
  2. 13 − 11 = 2
  3. 12 × 2 = 24

5 solutions

  • 12 × (1 × 13 − 11) = 24Steps
    1. 1 × 13 = 13
    2. 13 − 11 = 2
    3. 12 × 2 = 24
  • 12 × (13 − 11 ÷ 1) = 24Steps
    1. 11 ÷ 1 = 11
    2. 13 − 11 = 2
    3. 12 × 2 = 24
  • 12 × (13 ÷ 1 − 11) = 24Steps
    1. 13 ÷ 1 = 13
    2. 13 − 11 = 2
    3. 12 × 2 = 24
  • (13 − 11) ÷ (1 ÷ 12) = 24Steps
    1. 13 − 11 = 2
    2. 1 ÷ 12 = 1/12
    3. 2 ÷ 1/12 = 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 11 12 13 make 24?

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

How many solutions does 1 11 12 13 have?

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

How difficult is 1 11 12 13?

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).