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1 2 3 11 = 24: 5 solutions

Difficulty: HardOpen in Solver

2 × 11 − (1 − 3) = 24

  1. 2 × 11 = 22
  2. 1 − 3 = -2
  3. 22 − -2 = 24

5 solutions

  • 2 − 11 × (1 − 3) = 24Steps
    1. 1 − 3 = -2
    2. 11 × -2 = -22
    3. 2 − -22 = 24
  • 2 + 11 × (3 − 1) = 24Steps
    1. 3 − 1 = 2
    2. 11 × 2 = 22
    3. 2 + 22 = 24
  • (1 + 2) × (11 − 3) = 24Steps
    1. 1 + 2 = 3
    2. 11 − 3 = 8
    3. 3 × 8 = 24
  • 3 × (11 − (1 + 2)) = 24Steps
    1. 1 + 2 = 3
    2. 11 − 3 = 8
    3. 3 × 8 = 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 2 3 11 make 24?

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

How many solutions does 1 2 3 11 have?

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

How difficult is 1 2 3 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).