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1 2 4 12 = 24: 11 solutions

Difficulty: HardOpen in Solver

1 ÷ 2 × 4 × 12 = 24

  1. 1 ÷ 2 = 1/2
  2. 4 × 12 = 48
  3. 1/2 × 48 = 24

11 solutions

  • 12 + 4 × (1 + 2) = 24Steps
    1. 1 + 2 = 3
    2. 4 × 3 = 12
    3. 12 + 12 = 24
  • 4 × 12 ÷ (1 × 2) = 24Steps
    1. 4 × 12 = 48
    2. 1 × 2 = 2
    3. 48 ÷ 2 = 24
  • 12 × (4 − 1 × 2) = 24Steps
    1. 1 × 2 = 2
    2. 4 − 2 = 2
    3. 12 × 2 = 24
  • 12 × (1 × 4 − 2) = 24Steps
    1. 1 × 4 = 4
    2. 4 − 2 = 2
    3. 12 × 2 = 24
  • 1 × 12 × (4 − 2) = 24Steps
    1. 1 × 12 = 12
    2. 4 − 2 = 2
    3. 12 × 2 = 24
  • 12 × (4 − 2 ÷ 1) = 24Steps
    1. 2 ÷ 1 = 2
    2. 4 − 2 = 2
    3. 12 × 2 = 24
  • 12 ÷ (1 − 2 ÷ 4) = 24Steps
    1. 2 ÷ 4 = 1/2
    2. 1 − 1/2 = 1/2
    3. 12 ÷ 1/2 = 24
  • 12 × (4 ÷ 1 − 2) = 24Steps
    1. 4 ÷ 1 = 4
    2. 4 − 2 = 2
    3. 12 × 2 = 24
  • (1 + 2) × (12 − 4) = 24Steps
    1. 1 + 2 = 3
    2. 12 − 4 = 8
    3. 3 × 8 = 24
  • (4 − 2) ÷ (1 ÷ 12) = 24Steps
    1. 4 − 2 = 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 2 4 12 make 24?

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

How many solutions does 1 2 4 12 have?

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

How difficult is 1 2 4 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).