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3 4 6 12 = 24: 9 solutions

Difficulty: HardOpen in Solver

3 × 4 ÷ (6 ÷ 12) = 24

  1. 3 × 4 = 12
  2. 6 ÷ 12 = 1/2
  3. 12 ÷ 1/2 = 24

9 solutions

  • 4 × (3 + 6) − 12 = 24Steps
    1. 3 + 6 = 9
    2. 4 × 9 = 36
    3. 36 − 12 = 24
  • 12 − 4 × (3 − 6) = 24Steps
    1. 3 − 6 = -3
    2. 4 × -3 = -12
    3. 12 − -12 = 24
  • 4 × (3 × 6 − 12) = 24Steps
    1. 3 × 6 = 18
    2. 18 − 12 = 6
    3. 4 × 6 = 24
  • 12 + 4 × (6 − 3) = 24Steps
    1. 6 − 3 = 3
    2. 4 × 3 = 12
    3. 12 + 12 = 24
  • 12 × (4 − 6 ÷ 3) = 24Steps
    1. 6 ÷ 3 = 2
    2. 4 − 2 = 2
    3. 12 × 2 = 24
  • (6 + 12) ÷ (3 ÷ 4) = 24Steps
    1. 6 + 12 = 18
    2. 3 ÷ 4 = 3/4
    3. 18 ÷ 3/4 = 24
  • (3 − 6) × (4 − 12) = 24Steps
    1. 3 − 6 = -3
    2. 4 − 12 = -8
    3. -3 × -8 = 24
  • (6 − 3) × (12 − 4) = 24Steps
    1. 6 − 3 = 3
    2. 12 − 4 = 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 3 4 6 12 make 24?

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

How many solutions does 3 4 6 12 have?

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

How difficult is 3 4 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).