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3 6 9 10 = 24: 6 solutions

Difficulty: HardOpen in Solver

6 × 9 − 3 × 10 = 24

  1. 6 × 9 = 54
  2. 3 × 10 = 30
  3. 54 − 30 = 24

6 solutions

  • 6 × (10 + 3 − 9) = 24Steps
    1. 3 − 9 = -6
    2. 10 + -6 = 4
    3. 6 × 4 = 24
  • 10 ÷ (3 ÷ 9) − 6 = 24Steps
    1. 3 ÷ 9 = 1/3
    2. 10 ÷ 1/3 = 30
    3. 30 − 6 = 24
  • 9 × (6 − 10 ÷ 3) = 24Steps
    1. 10 ÷ 3 = 10/3
    2. 6 − 10/3 = 8/3
    3. 9 × 8/3 = 24
  • (3 − 9) × (6 − 10) = 24Steps
    1. 3 − 9 = -6
    2. 6 − 10 = -4
    3. -6 × -4 = 24
  • (9 − 3) × (10 − 6) = 24Steps
    1. 9 − 3 = 6
    2. 10 − 6 = 4
    3. 6 × 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 6 9 10 make 24?

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

How many solutions does 3 6 9 10 have?

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

How difficult is 3 6 9 10?

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).