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1 3 9 11 = 24: 8 solutions

Difficulty: HardOpen in Solver

1 + 3 + 9 + 11 = 24

  1. 1 + 3 = 4
  2. 9 + 11 = 20
  3. 4 + 20 = 24

8 solutions

  • 11 × 1 × 3 − 9 = 24Steps
    1. 1 × 3 = 3
    2. 11 × 3 = 33
    3. 33 − 9 = 24
  • 3 × 11 − 1 × 9 = 24Steps
    1. 3 × 11 = 33
    2. 1 × 9 = 9
    3. 33 − 9 = 24
  • 3 × 11 − 9 ÷ 1 = 24Steps
    1. 3 × 11 = 33
    2. 9 ÷ 1 = 9
    3. 33 − 9 = 24
  • 11 ÷ (1 ÷ 3) − 9 = 24Steps
    1. 1 ÷ 3 = 1/3
    2. 11 ÷ 1/3 = 33
    3. 33 − 9 = 24
  • 1 × (3 × 11 − 9) = 24Steps
    1. 3 × 11 = 33
    2. 33 − 9 = 24
    3. 1 × 24 = 24
  • (3 × 11 − 9) ÷ 1 = 24Steps
    1. 3 × 11 = 33
    2. 33 − 9 = 24
    3. 24 ÷ 1 = 24
  • 9 × (11 ÷ 3 − 1) = 24Steps
    1. 11 ÷ 3 = 11/3
    2. 11/3 − 1 = 8/3
    3. 9 × 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 1 3 9 11 make 24?

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

How many solutions does 1 3 9 11 have?

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

How difficult is 1 3 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).