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3 8 12 12 = 24: 7 solutions

Difficulty: HardOpen in Solver

3 × 8 + 12 − 12 = 24

  1. 3 × 8 = 24
  2. 12 − 12 = 0
  3. 24 + 0 = 24

7 solutions

  • 3 × 8 × 12 ÷ 12 = 24Steps
    1. 3 × 8 = 24
    2. 12 ÷ 12 = 1
    3. 24 × 1 = 24
  • 8 + 12 + 12 ÷ 3 = 24Steps
    1. 8 + 12 = 20
    2. 12 ÷ 3 = 4
    3. 20 + 4 = 24
  • 8 × (3 + 12 − 12) = 24Steps
    1. 3 + 12 = 15
    2. 15 − 12 = 3
    3. 8 × 3 = 24
  • 3 × (8 + 12 − 12) = 24Steps
    1. 8 + 12 = 20
    2. 20 − 12 = 8
    3. 3 × 8 = 24
  • 12 − 3 × (8 − 12) = 24Steps
    1. 8 − 12 = -4
    2. 3 × -4 = -12
    3. 12 − -12 = 24
  • 12 + 3 × (12 − 8) = 24Steps
    1. 12 − 8 = 4
    2. 3 × 4 = 12
    3. 12 + 12 = 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 8 12 12 make 24?

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

How many solutions does 3 8 12 12 have?

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

How difficult is 3 8 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).