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1 3 5 9 = 24: 9 solutions

Difficulty: EasyOpen in Solver

9 + 5 × 1 × 3 = 24

  1. 1 × 3 = 3
  2. 5 × 3 = 15
  3. 9 + 15 = 24

9 solutions

  • 1 × 9 + 3 × 5 = 24Steps
    1. 1 × 9 = 9
    2. 3 × 5 = 15
    3. 9 + 15 = 24
  • 3 × 5 + 9 ÷ 1 = 24Steps
    1. 3 × 5 = 15
    2. 9 ÷ 1 = 9
    3. 15 + 9 = 24
  • 9 + 5 ÷ (1 ÷ 3) = 24Steps
    1. 1 ÷ 3 = 1/3
    2. 5 ÷ 1/3 = 15
    3. 9 + 15 = 24
  • 1 × (9 + 3 × 5) = 24Steps
    1. 3 × 5 = 15
    2. 9 + 15 = 24
    3. 1 × 24 = 24
  • (9 + 3 × 5) ÷ 1 = 24Steps
    1. 3 × 5 = 15
    2. 9 + 15 = 24
    3. 24 ÷ 1 = 24
  • 9 × (1 + 5 ÷ 3) = 24Steps
    1. 5 ÷ 3 = 5/3
    2. 1 + 5/3 = 8/3
    3. 9 × 8/3 = 24
  • (1 − 5) × (3 − 9) = 24Steps
    1. 1 − 5 = -4
    2. 3 − 9 = -6
    3. -4 × -6 = 24
  • (5 − 1) × (9 − 3) = 24Steps
    1. 5 − 1 = 4
    2. 9 − 3 = 6
    3. 4 × 6 = 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 5 9 make 24?

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

How many solutions does 1 3 5 9 have?

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

How difficult is 1 3 5 9?

It is rated “Easy” 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).