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2 3 5 11 = 24: 9 solutions

Difficulty: HardOpen in Solver

2 × 5 + 3 + 11 = 24

  1. 2 × 5 = 10
  2. 3 + 11 = 14
  3. 10 + 14 = 24

9 solutions

  • 3 × (11 + 2 − 5) = 24Steps
    1. 2 − 5 = -3
    2. 11 + -3 = 8
    3. 3 × 8 = 24
  • 3 × 5 − (2 − 11) = 24Steps
    1. 3 × 5 = 15
    2. 2 − 11 = -9
    3. 15 − -9 = 24
  • 2 × 11 − (3 − 5) = 24Steps
    1. 2 × 11 = 22
    2. 3 − 5 = -2
    3. 22 − -2 = 24
  • 2 − 11 × (3 − 5) = 24Steps
    1. 3 − 5 = -2
    2. 11 × -2 = -22
    3. 2 − -22 = 24
  • 2 + 11 × (5 − 3) = 24Steps
    1. 5 − 3 = 2
    2. 11 × 2 = 22
    3. 2 + 22 = 24
  • (5 + 11) ÷ (2 ÷ 3) = 24Steps
    1. 5 + 11 = 16
    2. 2 ÷ 3 = 2/3
    3. 16 ÷ 2/3 = 24
  • (2 − 5) × (3 − 11) = 24Steps
    1. 2 − 5 = -3
    2. 3 − 11 = -8
    3. -3 × -8 = 24
  • (5 − 2) × (11 − 3) = 24Steps
    1. 5 − 2 = 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 2 3 5 11 make 24?

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

How many solutions does 2 3 5 11 have?

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

How difficult is 2 3 5 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).