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3 6 10 12 = 24: 8 solutions

Difficulty: HardOpen in Solver

3 × 10 + 6 − 12 = 24

  1. 3 × 10 = 30
  2. 6 − 12 = -6
  3. 30 + -6 = 24

8 solutions

  • 6 × 10 − 3 × 12 = 24Steps
    1. 6 × 10 = 60
    2. 3 × 12 = 36
    3. 60 − 36 = 24
  • 6 ÷ 3 + 10 + 12 = 24Steps
    1. 6 ÷ 3 = 2
    2. 10 + 12 = 22
    3. 2 + 22 = 24
  • 12 − 3 × (6 − 10) = 24Steps
    1. 6 − 10 = -4
    2. 3 × -4 = -12
    3. 12 − -12 = 24
  • 3 × (12 + 6 − 10) = 24Steps
    1. 6 − 10 = -4
    2. 12 + -4 = 8
    3. 3 × 8 = 24
  • (12 + 6 × 10) ÷ 3 = 24Steps
    1. 6 × 10 = 60
    2. 12 + 60 = 72
    3. 72 ÷ 3 = 24
  • 12 + 3 × (10 − 6) = 24Steps
    1. 10 − 6 = 4
    2. 3 × 4 = 12
    3. 12 + 12 = 24
  • 3 × (10 − 12 ÷ 6) = 24Steps
    1. 12 ÷ 6 = 2
    2. 10 − 2 = 8
    3. 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 6 10 12 make 24?

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

How many solutions does 3 6 10 12 have?

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

How difficult is 3 6 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).