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1 1 2 12 = 24: 7 solutions

Difficulty: HardOpen in Solver

1 − 1 + 2 × 12 = 24

  1. 1 − 1 = 0
  2. 2 × 12 = 24
  3. 0 + 24 = 24

7 solutions

  • 1 × 1 × 2 × 12 = 24Steps
    1. 1 × 1 = 1
    2. 2 × 12 = 24
    3. 1 × 24 = 24
  • 1 ÷ 1 × 2 × 12 = 24Steps
    1. 1 ÷ 1 = 1
    2. 2 × 12 = 24
    3. 1 × 24 = 24
  • 12 × (2 + 1 − 1) = 24Steps
    1. 1 − 1 = 0
    2. 2 + 0 = 2
    3. 12 × 2 = 24
  • 2 × (12 + 1 − 1) = 24Steps
    1. 1 − 1 = 0
    2. 12 + 0 = 12
    3. 2 × 12 = 24
  • 2 × 12 ÷ (1 × 1) = 24Steps
    1. 2 × 12 = 24
    2. 1 × 1 = 1
    3. 24 ÷ 1 = 24
  • 12 ÷ (1 − 1 ÷ 2) = 24Steps
    1. 1 ÷ 2 = 1/2
    2. 1 − 1/2 = 1/2
    3. 12 ÷ 1/2 = 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 1 2 12 make 24?

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

How many solutions does 1 1 2 12 have?

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

How difficult is 1 1 2 12?

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).