Skip to main content
24Point

Browse all solutions

1 5 7 12 = 24: 22 solutions

Difficulty: HardOpen in Solver

1 × 5 + 7 + 12 = 24

  1. 1 × 5 = 5
  2. 7 + 12 = 19
  3. 5 + 19 = 24

22 solutions

  • 1 × 7 + 5 + 12 = 24Steps
    1. 1 × 7 = 7
    2. 5 + 12 = 17
    3. 7 + 17 = 24
  • 1 − 12 + 5 × 7 = 24Steps
    1. 1 − 12 = -11
    2. 5 × 7 = 35
    3. -11 + 35 = 24
  • 1 × 12 + 5 + 7 = 24Steps
    1. 1 × 12 = 12
    2. 5 + 7 = 12
    3. 12 + 12 = 24
  • 5 ÷ 1 + 7 + 12 = 24Steps
    1. 5 ÷ 1 = 5
    2. 7 + 12 = 19
    3. 5 + 19 = 24
  • 5 + 7 + 12 ÷ 1 = 24Steps
    1. 5 + 7 = 12
    2. 12 ÷ 1 = 12
    3. 12 + 12 = 24
  • 5 + 12 + 7 ÷ 1 = 24Steps
    1. 5 + 12 = 17
    2. 7 ÷ 1 = 7
    3. 17 + 7 = 24
  • 12 × (7 − 1 × 5) = 24Steps
    1. 1 × 5 = 5
    2. 7 − 5 = 2
    3. 12 × 2 = 24
  • 12 × (1 × 7 − 5) = 24Steps
    1. 1 × 7 = 7
    2. 7 − 5 = 2
    3. 12 × 2 = 24
  • 1 × 12 × (7 − 5) = 24Steps
    1. 1 × 12 = 12
    2. 7 − 5 = 2
    3. 12 × 2 = 24
  • 12 × (7 − 5 ÷ 1) = 24Steps
    1. 5 ÷ 1 = 5
    2. 7 − 5 = 2
    3. 12 × 2 = 24
  • 12 + 1 × (5 + 7) = 24Steps
    1. 5 + 7 = 12
    2. 1 × 12 = 12
    3. 12 + 12 = 24
  • 1 × (12 + 5 + 7) = 24Steps
    1. 5 + 7 = 12
    2. 12 + 12 = 24
    3. 1 × 24 = 24
  • (12 + 5 + 7) ÷ 1 = 24Steps
    1. 5 + 7 = 12
    2. 12 + 12 = 24
    3. 24 ÷ 1 = 24
  • 12 + (5 + 7) ÷ 1 = 24Steps
    1. 5 + 7 = 12
    2. 12 ÷ 1 = 12
    3. 12 + 12 = 24
  • 7 + 1 × (5 + 12) = 24Steps
    1. 5 + 12 = 17
    2. 1 × 17 = 17
    3. 7 + 17 = 24
  • 7 + (5 + 12) ÷ 1 = 24Steps
    1. 5 + 12 = 17
    2. 17 ÷ 1 = 17
    3. 7 + 17 = 24
  • 12 × (7 ÷ 1 − 5) = 24Steps
    1. 7 ÷ 1 = 7
    2. 7 − 5 = 2
    3. 12 × 2 = 24
  • 5 + 1 × (7 + 12) = 24Steps
    1. 7 + 12 = 19
    2. 1 × 19 = 19
    3. 5 + 19 = 24
  • 5 + (7 + 12) ÷ 1 = 24Steps
    1. 7 + 12 = 19
    2. 19 ÷ 1 = 19
    3. 5 + 19 = 24
  • 5 × (12 − 7) − 1 = 24Steps
    1. 12 − 7 = 5
    2. 5 × 5 = 25
    3. 25 − 1 = 24
  • (7 − 5) ÷ (1 ÷ 12) = 24Steps
    1. 7 − 5 = 2
    2. 1 ÷ 12 = 1/12
    3. 2 ÷ 1/12 = 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 5 7 12 make 24?

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

How many solutions does 1 5 7 12 have?

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

How difficult is 1 5 7 12?

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).