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1 1 12 13 = 24: 18 solutions

Difficulty: HardOpen in Solver

12 + 13 − 1 × 1 = 24

  1. 12 + 13 = 25
  2. 1 × 1 = 1
  3. 25 − 1 = 24

18 solutions

  • 12 + 13 − 1 ÷ 1 = 24Steps
    1. 12 + 13 = 25
    2. 1 ÷ 1 = 1
    3. 25 − 1 = 24
  • 1 × 13 − (1 − 12) = 24Steps
    1. 1 × 13 = 13
    2. 1 − 12 = -11
    3. 13 − -11 = 24
  • 13 − 1 × (1 − 12) = 24Steps
    1. 1 − 12 = -11
    2. 1 × -11 = -11
    3. 13 − -11 = 24
  • 13 ÷ 1 − (1 − 12) = 24Steps
    1. 13 ÷ 1 = 13
    2. 1 − 12 = -11
    3. 13 − -11 = 24
  • 13 − (1 − 12) ÷ 1 = 24Steps
    1. 1 − 12 = -11
    2. -11 ÷ 1 = -11
    3. 13 − -11 = 24
  • 1 × 12 − (1 − 13) = 24Steps
    1. 1 × 12 = 12
    2. 1 − 13 = -12
    3. 12 − -12 = 24
  • 12 − 1 × (1 − 13) = 24Steps
    1. 1 − 13 = -12
    2. 1 × -12 = -12
    3. 12 − -12 = 24
  • 12 ÷ 1 − (1 − 13) = 24Steps
    1. 12 ÷ 1 = 12
    2. 1 − 13 = -12
    3. 12 − -12 = 24
  • 12 − (1 − 13) ÷ 1 = 24Steps
    1. 1 − 13 = -12
    2. -12 ÷ 1 = -12
    3. 12 − -12 = 24
  • 13 + 1 × (12 − 1) = 24Steps
    1. 12 − 1 = 11
    2. 1 × 11 = 11
    3. 13 + 11 = 24
  • 13 + (12 − 1) ÷ 1 = 24Steps
    1. 12 − 1 = 11
    2. 11 ÷ 1 = 11
    3. 13 + 11 = 24
  • 1 × (12 + 13) − 1 = 24Steps
    1. 12 + 13 = 25
    2. 1 × 25 = 25
    3. 25 − 1 = 24
  • (12 + 13) ÷ 1 − 1 = 24Steps
    1. 12 + 13 = 25
    2. 25 ÷ 1 = 25
    3. 25 − 1 = 24
  • 12 + 1 × (13 − 1) = 24Steps
    1. 13 − 1 = 12
    2. 1 × 12 = 12
    3. 12 + 12 = 24
  • 12 + (13 − 1) ÷ 1 = 24Steps
    1. 13 − 1 = 12
    2. 12 ÷ 1 = 12
    3. 12 + 12 = 24
  • 1 × (13 − (1 − 12)) = 24Steps
    1. 1 − 12 = -11
    2. 13 − -11 = 24
    3. 1 × 24 = 24
  • (13 − (1 − 12)) ÷ 1 = 24Steps
    1. 1 − 12 = -11
    2. 13 − -11 = 24
    3. 24 ÷ 1 = 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 12 13 make 24?

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

How many solutions does 1 1 12 13 have?

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

How difficult is 1 1 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).