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4 4 7 12 = 24: 6 solutions

Difficulty: HardOpen in Solver

12 − 4 × (4 − 7) = 24

  1. 4 − 7 = -3
  2. 4 × -3 = -12
  3. 12 − -12 = 24

6 solutions

  • 12 + 4 × (7 − 4) = 24Steps
    1. 7 − 4 = 3
    2. 4 × 3 = 12
    3. 12 + 12 = 24
  • 4 − 4 × (7 − 12) = 24Steps
    1. 7 − 12 = -5
    2. 4 × -5 = -20
    3. 4 − -20 = 24
  • 4 + 4 × (12 − 7) = 24Steps
    1. 12 − 7 = 5
    2. 4 × 5 = 20
    3. 4 + 20 = 24
  • (4 − 7) × (4 − 12) = 24Steps
    1. 4 − 7 = -3
    2. 4 − 12 = -8
    3. -3 × -8 = 24
  • (7 − 4) × (12 − 4) = 24Steps
    1. 7 − 4 = 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 4 4 7 12 make 24?

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

How many solutions does 4 4 7 12 have?

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

How difficult is 4 4 7 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).