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4 4 6 12 = 24: 7 solutions

Difficulty: HardOpen in Solver

4 × 12 − 4 × 6 = 24

  1. 4 × 12 = 48
  2. 4 × 6 = 24
  3. 48 − 24 = 24

7 solutions

  • 12 × (4 + 4 − 6) = 24Steps
    1. 4 + 4 = 8
    2. 8 − 6 = 2
    3. 12 × 2 = 24
  • 6 × (4 × 4 − 12) = 24Steps
    1. 4 × 4 = 16
    2. 16 − 12 = 4
    3. 6 × 4 = 24
  • 4 × 12 ÷ (6 − 4) = 24Steps
    1. 4 × 12 = 48
    2. 6 − 4 = 2
    3. 48 ÷ 2 = 24
  • 4 × (4 + 12 ÷ 6) = 24Steps
    1. 12 ÷ 6 = 2
    2. 4 + 2 = 6
    3. 4 × 6 = 24
  • 6 × (12 − (4 + 4)) = 24Steps
    1. 4 + 4 = 8
    2. 12 − 8 = 4
    3. 6 × 4 = 24
  • (4 + 12) ÷ (4 ÷ 6) = 24Steps
    1. 4 + 12 = 16
    2. 4 ÷ 6 = 2/3
    3. 16 ÷ 2/3 = 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 4 4 6 12 make 24?

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

How many solutions does 4 4 6 12 have?

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

How difficult is 4 4 6 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).