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3 6 9 11 = 24: 6 solutions

Difficulty: HardOpen in Solver

11 × (6 − 3) − 9 = 24

  1. 6 − 3 = 3
  2. 11 × 3 = 33
  3. 33 − 9 = 24

6 solutions

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

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

How many solutions does 3 6 9 11 have?

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

How difficult is 3 6 9 11?

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).