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5 6 9 12 = 24: 3 solutions

Difficulty: HardOpen in Solver

12 × (5 + 6 − 9) = 24

  1. 5 + 6 = 11
  2. 11 − 9 = 2
  3. 12 × 2 = 24

3 solutions

  • (5 − 9) × (6 − 12) = 24Steps
    1. 5 − 9 = -4
    2. 6 − 12 = -6
    3. -4 × -6 = 24
  • (9 − 5) × (12 − 6) = 24Steps
    1. 9 − 5 = 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 5 6 9 12 make 24?

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

How many solutions does 5 6 9 12 have?

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

How difficult is 5 6 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).