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1 4 7 13 = 24: 20 solutions

Difficulty: HardOpen in Solver

1 × 4 + 7 + 13 = 24

  1. 1 × 4 = 4
  2. 7 + 13 = 20
  3. 4 + 20 = 24

20 solutions

  • 1 × 7 + 4 + 13 = 24Steps
    1. 1 × 7 = 7
    2. 4 + 13 = 17
    3. 7 + 17 = 24
  • 1 × 13 + 4 + 7 = 24Steps
    1. 1 × 13 = 13
    2. 4 + 7 = 11
    3. 13 + 11 = 24
  • 4 ÷ 1 + 7 + 13 = 24Steps
    1. 4 ÷ 1 = 4
    2. 7 + 13 = 20
    3. 4 + 20 = 24
  • 4 + 7 + 13 ÷ 1 = 24Steps
    1. 4 + 7 = 11
    2. 13 ÷ 1 = 13
    3. 11 + 13 = 24
  • 4 + 13 + 7 ÷ 1 = 24Steps
    1. 4 + 13 = 17
    2. 7 ÷ 1 = 7
    3. 17 + 7 = 24
  • 1 × 4 × (13 − 7) = 24Steps
    1. 1 × 4 = 4
    2. 13 − 7 = 6
    3. 4 × 6 = 24
  • 4 × (13 − 1 × 7) = 24Steps
    1. 1 × 7 = 7
    2. 13 − 7 = 6
    3. 4 × 6 = 24
  • 4 × (1 × 13 − 7) = 24Steps
    1. 1 × 13 = 13
    2. 13 − 7 = 6
    3. 4 × 6 = 24
  • 13 + 1 × (4 + 7) = 24Steps
    1. 4 + 7 = 11
    2. 1 × 11 = 11
    3. 13 + 11 = 24
  • 1 × (13 + 4 + 7) = 24Steps
    1. 4 + 7 = 11
    2. 13 + 11 = 24
    3. 1 × 24 = 24
  • (13 + 4 + 7) ÷ 1 = 24Steps
    1. 4 + 7 = 11
    2. 13 + 11 = 24
    3. 24 ÷ 1 = 24
  • 13 + (4 + 7) ÷ 1 = 24Steps
    1. 4 + 7 = 11
    2. 11 ÷ 1 = 11
    3. 13 + 11 = 24
  • 7 + 1 × (4 + 13) = 24Steps
    1. 4 + 13 = 17
    2. 1 × 17 = 17
    3. 7 + 17 = 24
  • 7 + (4 + 13) ÷ 1 = 24Steps
    1. 4 + 13 = 17
    2. 17 ÷ 1 = 17
    3. 7 + 17 = 24
  • 4 × (13 − 7 ÷ 1) = 24Steps
    1. 7 ÷ 1 = 7
    2. 13 − 7 = 6
    3. 4 × 6 = 24
  • 4 + 1 × (7 + 13) = 24Steps
    1. 7 + 13 = 20
    2. 1 × 20 = 20
    3. 4 + 20 = 24
  • 4 + (7 + 13) ÷ 1 = 24Steps
    1. 7 + 13 = 20
    2. 20 ÷ 1 = 20
    3. 4 + 20 = 24
  • 4 × (13 ÷ 1 − 7) = 24Steps
    1. 13 ÷ 1 = 13
    2. 13 − 7 = 6
    3. 4 × 6 = 24
  • (13 − 7) ÷ (1 ÷ 4) = 24Steps
    1. 13 − 7 = 6
    2. 1 ÷ 4 = 1/4
    3. 6 ÷ 1/4 = 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 4 7 13 make 24?

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

How many solutions does 1 4 7 13 have?

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

How difficult is 1 4 7 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).