Skip to main content
24Point

Browse all solutions

1 3 5 13 = 24: 8 solutions

Difficulty: HardOpen in Solver

1 × 3 × (13 − 5) = 24

  1. 1 × 3 = 3
  2. 13 − 5 = 8
  3. 3 × 8 = 24

8 solutions

  • 3 × (13 − 1 × 5) = 24Steps
    1. 1 × 5 = 5
    2. 13 − 5 = 8
    3. 3 × 8 = 24
  • 3 × (1 × 13 − 5) = 24Steps
    1. 1 × 13 = 13
    2. 13 − 5 = 8
    3. 3 × 8 = 24
  • 3 × (13 − 5 ÷ 1) = 24Steps
    1. 5 ÷ 1 = 5
    2. 13 − 5 = 8
    3. 3 × 8 = 24
  • 3 × (13 ÷ 1 − 5) = 24Steps
    1. 13 ÷ 1 = 13
    2. 13 − 5 = 8
    3. 3 × 8 = 24
  • (13 − 5) ÷ (1 ÷ 3) = 24Steps
    1. 13 − 5 = 8
    2. 1 ÷ 3 = 1/3
    3. 8 ÷ 1/3 = 24
  • (1 − 13) × (3 − 5) = 24Steps
    1. 1 − 13 = -12
    2. 3 − 5 = -2
    3. -12 × -2 = 24
  • (5 − 3) × (13 − 1) = 24Steps
    1. 5 − 3 = 2
    2. 13 − 1 = 12
    3. 2 × 12 = 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 13 make 24?

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

How many solutions does 1 3 5 13 have?

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

How difficult is 1 3 5 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).