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3 7 9 12 = 24: 6 solutions

Difficulty: HardOpen in Solver

3 × 7 − (9 − 12) = 24

  1. 3 × 7 = 21
  2. 9 − 12 = -3
  3. 21 − -3 = 24

6 solutions

  • 9 × (7 − 3) − 12 = 24Steps
    1. 7 − 3 = 4
    2. 9 × 4 = 36
    3. 36 − 12 = 24
  • 9 − 3 × (7 − 12) = 24Steps
    1. 7 − 12 = -5
    2. 3 × -5 = -15
    3. 9 − -15 = 24
  • 3 − 7 × (9 − 12) = 24Steps
    1. 9 − 12 = -3
    2. 7 × -3 = -21
    3. 3 − -21 = 24
  • 9 + 3 × (12 − 7) = 24Steps
    1. 12 − 7 = 5
    2. 3 × 5 = 15
    3. 9 + 15 = 24
  • 3 + 7 × (12 − 9) = 24Steps
    1. 12 − 9 = 3
    2. 7 × 3 = 21
    3. 3 + 21 = 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 7 9 12 make 24?

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

How many solutions does 3 7 9 12 have?

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

How difficult is 3 7 9 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).