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3 5 6 9 = 24: 9 solutions

Difficulty: EasyOpen in Solver

3 − 9 + 5 × 6 = 24

  1. 3 − 9 = -6
  2. 5 × 6 = 30
  3. -6 + 30 = 24

9 solutions

  • 6 − 9 × (3 − 5) = 24Steps
    1. 3 − 5 = -2
    2. 9 × -2 = -18
    3. 6 − -18 = 24
  • 9 − 5 × (3 − 6) = 24Steps
    1. 3 − 6 = -3
    2. 5 × -3 = -15
    3. 9 − -15 = 24
  • 6 + 9 × (5 − 3) = 24Steps
    1. 5 − 3 = 2
    2. 9 × 2 = 18
    3. 6 + 18 = 24
  • 3 × (5 + 6) − 9 = 24Steps
    1. 5 + 6 = 11
    2. 3 × 11 = 33
    3. 33 − 9 = 24
  • 3 × (9 + 5 − 6) = 24Steps
    1. 5 − 6 = -1
    2. 9 + -1 = 8
    3. 3 × 8 = 24
  • 9 + 5 × (6 − 3) = 24Steps
    1. 6 − 3 = 3
    2. 5 × 3 = 15
    3. 9 + 15 = 24
  • 5 × (9 − 3) − 6 = 24Steps
    1. 9 − 3 = 6
    2. 5 × 6 = 30
    3. 30 − 6 = 24
  • (3 + 5) × (9 − 6) = 24Steps
    1. 3 + 5 = 8
    2. 9 − 6 = 3
    3. 8 × 3 = 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 5 6 9 make 24?

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

How many solutions does 3 5 6 9 have?

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

How difficult is 3 5 6 9?

It is rated “Easy” 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).