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7 8 12 13 = 24: 4 solutions

Difficulty: HardOpen in Solver

7 − 8 + 12 + 13 = 24

  1. 7 − 8 = -1
  2. 12 + 13 = 25
  3. -1 + 25 = 24

4 solutions

  • 12 × (7 + 8 − 13) = 24Steps
    1. 7 + 8 = 15
    2. 15 − 13 = 2
    3. 12 × 2 = 24
  • (7 − 13) × (8 − 12) = 24Steps
    1. 7 − 13 = -6
    2. 8 − 12 = -4
    3. -6 × -4 = 24
  • (12 − 8) × (13 − 7) = 24Steps
    1. 12 − 8 = 4
    2. 13 − 7 = 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 7 8 12 13 make 24?

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

How many solutions does 7 8 12 13 have?

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

How difficult is 7 8 12 13?

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).