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1 3 6 12 = 24: 7 solutions

Difficulty: HardOpen in Solver

1 ÷ 3 × 6 × 12 = 24

  1. 1 ÷ 3 = 1/3
  2. 6 × 12 = 72
  3. 1/3 × 72 = 24

7 solutions

  • 12 − 6 × (1 − 3) = 24Steps
    1. 1 − 3 = -2
    2. 6 × -2 = -12
    3. 12 − -12 = 24
  • 6 × 12 ÷ (1 × 3) = 24Steps
    1. 6 × 12 = 72
    2. 1 × 3 = 3
    3. 72 ÷ 3 = 24
  • 12 + 6 × (3 − 1) = 24Steps
    1. 3 − 1 = 2
    2. 6 × 2 = 12
    3. 12 + 12 = 24
  • 12 ÷ (1 − 3 ÷ 6) = 24Steps
    1. 3 ÷ 6 = 1/2
    2. 1 − 1/2 = 1/2
    3. 12 ÷ 1/2 = 24
  • 12 × (6 − (1 + 3)) = 24Steps
    1. 1 + 3 = 4
    2. 6 − 4 = 2
    3. 12 × 2 = 24
  • (1 + 3) × (12 − 6) = 24Steps
    1. 1 + 3 = 4
    2. 12 − 6 = 6
    3. 4 × 6 = 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 3 6 12 make 24?

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

How many solutions does 1 3 6 12 have?

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

How difficult is 1 3 6 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).