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1 8 9 12 = 24: 8 solutions

Difficulty: HardOpen in Solver

12 × (9 + 1 − 8) = 24

  1. 1 − 8 = -7
  2. 9 + -7 = 2
  3. 12 × 2 = 24

8 solutions

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

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

How many solutions does 1 8 9 12 have?

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

How difficult is 1 8 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).