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4 9 12 12 = 24: 6 solutions

Difficulty: HardOpen in Solver

9 + 12 + 12 ÷ 4 = 24

  1. 9 + 12 = 21
  2. 12 ÷ 4 = 3
  3. 21 + 3 = 24

6 solutions

  • 12 − 4 × (9 − 12) = 24Steps
    1. 9 − 12 = -3
    2. 4 × -3 = -12
    3. 12 − -12 = 24
  • (9 × 12 − 12) ÷ 4 = 24Steps
    1. 9 × 12 = 108
    2. 108 − 12 = 96
    3. 96 ÷ 4 = 24
  • 12 + 4 × (12 − 9) = 24Steps
    1. 12 − 9 = 3
    2. 4 × 3 = 12
    3. 12 + 12 = 24
  • (4 − 12) × (9 − 12) = 24Steps
    1. 4 − 12 = -8
    2. 9 − 12 = -3
    3. -8 × -3 = 24
  • (12 − 4) × (12 − 9) = 24Steps
    1. 12 − 4 = 8
    2. 12 − 9 = 3
    3. 8 × 3 = 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 4 9 12 12 make 24?

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

How many solutions does 4 9 12 12 have?

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

How difficult is 4 9 12 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).