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3 8 11 11 = 24: 6 solutions

Difficulty: HardOpen in Solver

3 × 8 + 11 − 11 = 24

  1. 3 × 8 = 24
  2. 11 − 11 = 0
  3. 24 + 0 = 24

6 solutions

  • 3 × 8 × 11 ÷ 11 = 24Steps
    1. 3 × 8 = 24
    2. 11 ÷ 11 = 1
    3. 24 × 1 = 24
  • 8 × (3 + 11 − 11) = 24Steps
    1. 3 + 11 = 14
    2. 14 − 11 = 3
    3. 8 × 3 = 24
  • 3 × (8 + 11 − 11) = 24Steps
    1. 8 + 11 = 19
    2. 19 − 11 = 8
    3. 3 × 8 = 24
  • (3 − 11) × (8 − 11) = 24Steps
    1. 3 − 11 = -8
    2. 8 − 11 = -3
    3. -8 × -3 = 24
  • (11 − 3) × (11 − 8) = 24Steps
    1. 11 − 3 = 8
    2. 11 − 8 = 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 8 11 11 make 24?

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

How many solutions does 3 8 11 11 have?

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

How difficult is 3 8 11 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).