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3 5 9 13 = 24: 3 solutions

Difficulty: HardOpen in Solver

9 + 13 − (3 − 5) = 24

  1. 9 + 13 = 22
  2. 3 − 5 = -2
  3. 22 − -2 = 24

3 solutions

  • (3 + 9 × 13) ÷ 5 = 24Steps
    1. 9 × 13 = 117
    2. 3 + 117 = 120
    3. 120 ÷ 5 = 24
  • (13 − 5) ÷ (3 ÷ 9) = 24Steps
    1. 13 − 5 = 8
    2. 3 ÷ 9 = 1/3
    3. 8 ÷ 1/3 = 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 9 13 make 24?

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

How many solutions does 3 5 9 13 have?

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

How difficult is 3 5 9 13?

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).