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3 4 9 12 = 24: 7 solutions

Difficulty: HardOpen in Solver

3 × 9 − 12 ÷ 4 = 24

  1. 3 × 9 = 27
  2. 12 ÷ 4 = 3
  3. 27 − 3 = 24

7 solutions

  • 12 + 9 ÷ (3 ÷ 4) = 24Steps
    1. 3 ÷ 4 = 3/4
    2. 9 ÷ 3/4 = 12
    3. 12 + 12 = 24
  • 4 × (12 + 3 − 9) = 24Steps
    1. 3 − 9 = -6
    2. 12 + -6 = 6
    3. 4 × 6 = 24
  • 12 ÷ (4 ÷ 9) − 3 = 24Steps
    1. 4 ÷ 9 = 4/9
    2. 12 ÷ 4/9 = 27
    3. 27 − 3 = 24
  • 9 × (3 − 4 ÷ 12) = 24Steps
    1. 4 ÷ 12 = 1/3
    2. 3 − 1/3 = 8/3
    3. 9 × 8/3 = 24
  • 12 × (9 − (3 + 4)) = 24Steps
    1. 3 + 4 = 7
    2. 9 − 7 = 2
    3. 12 × 2 = 24
  • (12 − 4) ÷ (3 ÷ 9) = 24Steps
    1. 12 − 4 = 8
    2. 3 ÷ 9 = 1/3
    3. 8 ÷ 1/3 = 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 3 4 9 12 make 24?

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

How many solutions does 3 4 9 12 have?

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

How difficult is 3 4 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).