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2 4 8 12 = 24: 8 solutions

Difficulty: HardOpen in Solver

4 × (12 + 2 − 8) = 24

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

8 solutions

  • 2 × 8 − (4 − 12) = 24Steps
    1. 2 × 8 = 16
    2. 4 − 12 = -8
    3. 16 − -8 = 24
  • 2 × (4 + 12) − 8 = 24Steps
    1. 4 + 12 = 16
    2. 2 × 16 = 32
    3. 32 − 8 = 24
  • 8 − 2 × (4 − 12) = 24Steps
    1. 4 − 12 = -8
    2. 2 × -8 = -16
    3. 8 − -16 = 24
  • 8 + 2 × (12 − 4) = 24Steps
    1. 12 − 4 = 8
    2. 2 × 8 = 16
    3. 8 + 16 = 24
  • 12 × (8 − (2 + 4)) = 24Steps
    1. 2 + 4 = 6
    2. 8 − 6 = 2
    3. 12 × 2 = 24
  • (2 + 4) × (12 − 8) = 24Steps
    1. 2 + 4 = 6
    2. 12 − 8 = 4
    3. 6 × 4 = 24
  • (8 − 4) ÷ (2 ÷ 12) = 24Steps
    1. 8 − 4 = 4
    2. 2 ÷ 12 = 1/6
    3. 4 ÷ 1/6 = 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 2 4 8 12 make 24?

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

How many solutions does 2 4 8 12 have?

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

How difficult is 2 4 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).