Skip to main content
24Point

Browse all solutions

1 4 8 12 = 24: 18 solutions

Difficulty: HardOpen in Solver

1 × 4 + 8 + 12 = 24

  1. 1 × 4 = 4
  2. 8 + 12 = 20
  3. 4 + 20 = 24

18 solutions

  • 1 ÷ 4 × 8 × 12 = 24Steps
    1. 1 ÷ 4 = 1/4
    2. 8 × 12 = 96
    3. 1/4 × 96 = 24
  • 1 × 8 + 4 + 12 = 24Steps
    1. 1 × 8 = 8
    2. 4 + 12 = 16
    3. 8 + 16 = 24
  • 1 × 12 + 4 + 8 = 24Steps
    1. 1 × 12 = 12
    2. 4 + 8 = 12
    3. 12 + 12 = 24
  • 4 ÷ 1 + 8 + 12 = 24Steps
    1. 4 ÷ 1 = 4
    2. 8 + 12 = 20
    3. 4 + 20 = 24
  • 4 + 8 + 12 ÷ 1 = 24Steps
    1. 4 + 8 = 12
    2. 12 ÷ 1 = 12
    3. 12 + 12 = 24
  • 4 + 12 + 8 ÷ 1 = 24Steps
    1. 4 + 12 = 16
    2. 8 ÷ 1 = 8
    3. 16 + 8 = 24
  • 8 × 12 ÷ (1 × 4) = 24Steps
    1. 8 × 12 = 96
    2. 1 × 4 = 4
    3. 96 ÷ 4 = 24
  • 4 × (1 + 8) − 12 = 24Steps
    1. 1 + 8 = 9
    2. 4 × 9 = 36
    3. 36 − 12 = 24
  • 12 + 1 × (4 + 8) = 24Steps
    1. 4 + 8 = 12
    2. 1 × 12 = 12
    3. 12 + 12 = 24
  • 1 × (12 + 4 + 8) = 24Steps
    1. 4 + 8 = 12
    2. 12 + 12 = 24
    3. 1 × 24 = 24
  • (12 + 4 + 8) ÷ 1 = 24Steps
    1. 4 + 8 = 12
    2. 12 + 12 = 24
    3. 24 ÷ 1 = 24
  • 12 + (4 + 8) ÷ 1 = 24Steps
    1. 4 + 8 = 12
    2. 12 ÷ 1 = 12
    3. 12 + 12 = 24
  • 12 ÷ (1 − 4 ÷ 8) = 24Steps
    1. 4 ÷ 8 = 1/2
    2. 1 − 1/2 = 1/2
    3. 12 ÷ 1/2 = 24
  • 8 + 1 × (4 + 12) = 24Steps
    1. 4 + 12 = 16
    2. 1 × 16 = 16
    3. 8 + 16 = 24
  • 8 + (4 + 12) ÷ 1 = 24Steps
    1. 4 + 12 = 16
    2. 16 ÷ 1 = 16
    3. 8 + 16 = 24
  • 4 + 1 × (8 + 12) = 24Steps
    1. 8 + 12 = 20
    2. 1 × 20 = 20
    3. 4 + 20 = 24
  • 4 + (8 + 12) ÷ 1 = 24Steps
    1. 8 + 12 = 20
    2. 20 ÷ 1 = 20
    3. 4 + 20 = 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 1 4 8 12 make 24?

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

How many solutions does 1 4 8 12 have?

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

How difficult is 1 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).