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11 12 13 13 = 24: 11 solutions

Difficulty: HardOpen in Solver

11 + 12 + 13 ÷ 13 = 24

  1. 11 + 12 = 23
  2. 13 ÷ 13 = 1
  3. 23 + 1 = 24

11 solutions

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

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

How many solutions does 11 12 13 13 have?

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

How difficult is 11 12 13 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).