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4 6 8 12 = 24: 8 solutions

Difficulty: HardOpen in Solver

12 × (4 + 6 − 8) = 24

  1. 4 + 6 = 10
  2. 10 − 8 = 2
  3. 12 × 2 = 24

8 solutions

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

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

How many solutions does 4 6 8 12 have?

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

How difficult is 4 6 8 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).