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3 4 10 12 = 24: 5 solutions

Difficulty: HardOpen in Solver

3 × 4 × (12 − 10) = 24

  1. 3 × 4 = 12
  2. 12 − 10 = 2
  3. 12 × 2 = 24

5 solutions

  • 12 × (3 × 4 − 10) = 24Steps
    1. 3 × 4 = 12
    2. 12 − 10 = 2
    3. 12 × 2 = 24
  • 12 ÷ (3 − 10 ÷ 4) = 24Steps
    1. 10 ÷ 4 = 5/2
    2. 3 − 5/2 = 1/2
    3. 12 ÷ 1/2 = 24
  • 4 × (10 − 12 ÷ 3) = 24Steps
    1. 12 ÷ 3 = 4
    2. 10 − 4 = 6
    3. 4 × 6 = 24
  • (10 − 4) ÷ (3 ÷ 12) = 24Steps
    1. 10 − 4 = 6
    2. 3 ÷ 12 = 1/4
    3. 6 ÷ 1/4 = 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 4 10 12 make 24?

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

How many solutions does 3 4 10 12 have?

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

How difficult is 3 4 10 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).