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3 4 5 12 = 24: 8 solutions

Difficulty: HardOpen in Solver

3 + 4 + 5 + 12 = 24

  1. 3 + 4 = 7
  2. 5 + 12 = 17
  3. 7 + 17 = 24

8 solutions

  • 4 × 5 + 12 ÷ 3 = 24Steps
    1. 4 × 5 = 20
    2. 12 ÷ 3 = 4
    3. 20 + 4 = 24
  • 12 × (3 + 4 − 5) = 24Steps
    1. 3 + 4 = 7
    2. 7 − 5 = 2
    3. 12 × 2 = 24
  • 4 + 12 ÷ (3 ÷ 5) = 24Steps
    1. 3 ÷ 5 = 3/5
    2. 12 ÷ 3/5 = 20
    3. 4 + 20 = 24
  • 3 × (4 × 5 − 12) = 24Steps
    1. 4 × 5 = 20
    2. 20 − 12 = 8
    3. 3 × 8 = 24
  • 4 × 12 ÷ (5 − 3) = 24Steps
    1. 4 × 12 = 48
    2. 5 − 3 = 2
    3. 48 ÷ 2 = 24
  • 3 × (5 + 12 ÷ 4) = 24Steps
    1. 12 ÷ 4 = 3
    2. 5 + 3 = 8
    3. 3 × 8 = 24
  • (3 + 5) ÷ (4 ÷ 12) = 24Steps
    1. 3 + 5 = 8
    2. 4 ÷ 12 = 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 5 12 make 24?

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

How many solutions does 3 4 5 12 have?

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

How difficult is 3 4 5 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).