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3 3 8 12 = 24: 4 solutions

Difficulty: HardOpen in Solver

8 × (12 − 3 × 3) = 24

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

4 solutions

  • 12 × (8 − (3 + 3)) = 24Steps
    1. 3 + 3 = 6
    2. 8 − 6 = 2
    3. 12 × 2 = 24
  • (3 + 3) × (12 − 8) = 24Steps
    1. 3 + 3 = 6
    2. 12 − 8 = 4
    3. 6 × 4 = 24
  • (12 − 3) ÷ (3 ÷ 8) = 24Steps
    1. 12 − 3 = 9
    2. 3 ÷ 8 = 3/8
    3. 9 ÷ 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 3 3 8 12 make 24?

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

How many solutions does 3 3 8 12 have?

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

How difficult is 3 3 8 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).