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1 3 9 12 = 24: 17 solutions

Difficulty: HardOpen in Solver

1 × 3 + 9 + 12 = 24

  1. 1 × 3 = 3
  2. 9 + 12 = 21
  3. 3 + 21 = 24

17 solutions

  • 1 × 9 + 3 + 12 = 24Steps
    1. 1 × 9 = 9
    2. 3 + 12 = 15
    3. 9 + 15 = 24
  • 1 × 12 + 3 + 9 = 24Steps
    1. 1 × 12 = 12
    2. 3 + 9 = 12
    3. 12 + 12 = 24
  • 3 ÷ 1 + 9 + 12 = 24Steps
    1. 3 ÷ 1 = 3
    2. 9 + 12 = 21
    3. 3 + 21 = 24
  • 3 + 9 + 12 ÷ 1 = 24Steps
    1. 3 + 9 = 12
    2. 12 ÷ 1 = 12
    3. 12 + 12 = 24
  • 3 + 12 + 9 ÷ 1 = 24Steps
    1. 3 + 12 = 15
    2. 9 ÷ 1 = 9
    3. 15 + 9 = 24
  • 9 × (1 + 3) − 12 = 24Steps
    1. 1 + 3 = 4
    2. 9 × 4 = 36
    3. 36 − 12 = 24
  • 12 + 1 × (3 + 9) = 24Steps
    1. 3 + 9 = 12
    2. 1 × 12 = 12
    3. 12 + 12 = 24
  • 1 × (12 + 3 + 9) = 24Steps
    1. 3 + 9 = 12
    2. 12 + 12 = 24
    3. 1 × 24 = 24
  • (12 + 3 + 9) ÷ 1 = 24Steps
    1. 3 + 9 = 12
    2. 12 + 12 = 24
    3. 24 ÷ 1 = 24
  • 12 + (3 + 9) ÷ 1 = 24Steps
    1. 3 + 9 = 12
    2. 12 ÷ 1 = 12
    3. 12 + 12 = 24
  • 9 + 1 × (3 + 12) = 24Steps
    1. 3 + 12 = 15
    2. 1 × 15 = 15
    3. 9 + 15 = 24
  • 9 + (3 + 12) ÷ 1 = 24Steps
    1. 3 + 12 = 15
    2. 15 ÷ 1 = 15
    3. 9 + 15 = 24
  • 12 × (9 ÷ 3 − 1) = 24Steps
    1. 9 ÷ 3 = 3
    2. 3 − 1 = 2
    3. 12 × 2 = 24
  • 3 + 1 × (9 + 12) = 24Steps
    1. 9 + 12 = 21
    2. 1 × 21 = 21
    3. 3 + 21 = 24
  • 3 + (9 + 12) ÷ 1 = 24Steps
    1. 9 + 12 = 21
    2. 21 ÷ 1 = 21
    3. 3 + 21 = 24
  • 3 × (12 − 1) − 9 = 24Steps
    1. 12 − 1 = 11
    2. 3 × 11 = 33
    3. 33 − 9 = 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 9 12 make 24?

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

How many solutions does 1 3 9 12 have?

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

How difficult is 1 3 9 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).