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8 9 12 12 = 24: 8 solutions

Difficulty: HardOpen in Solver

12 − 12 × (8 − 9) = 24

  1. 8 − 9 = -1
  2. 12 × -1 = -12
  3. 12 − -12 = 24

8 solutions

  • 12 − 12 ÷ (8 − 9) = 24Steps
    1. 8 − 9 = -1
    2. 12 ÷ -1 = -12
    3. 12 − -12 = 24
  • 12 + 12 × (9 − 8) = 24Steps
    1. 9 − 8 = 1
    2. 12 × 1 = 12
    3. 12 + 12 = 24
  • 12 + 12 ÷ (9 − 8) = 24Steps
    1. 9 − 8 = 1
    2. 12 ÷ 1 = 12
    3. 12 + 12 = 24
  • 8 + 12 ÷ (9 ÷ 12) = 24Steps
    1. 9 ÷ 12 = 3/4
    2. 12 ÷ 3/4 = 16
    3. 8 + 16 = 24
  • 9 × (12 − 8) − 12 = 24Steps
    1. 12 − 8 = 4
    2. 9 × 4 = 36
    3. 36 − 12 = 24
  • (9 − 8) × (12 + 12) = 24Steps
    1. 9 − 8 = 1
    2. 12 + 12 = 24
    3. 1 × 24 = 24
  • (12 + 12) ÷ (9 − 8) = 24Steps
    1. 12 + 12 = 24
    2. 9 − 8 = 1
    3. 24 ÷ 1 = 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 8 9 12 12 make 24?

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

How many solutions does 8 9 12 12 have?

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

How difficult is 8 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).