Use four supplied numbers once each to make twenty-four with arithmetic and brackets.
Use the four supplied numbers exactly once each. Addition, subtraction, multiplication, division and brackets are allowed. You may change their order. Joining digits into a larger number, adding extra digits, using powers or factorials, and dividing by zero are not allowed. Intermediate fractions and negative numbers are permitted, although the four starter cards have answers that do not need complicated fractions.
The four cards are 1–2–3–4, 2–3–4–6, 4–4–4–4 and 2–2–3–3. Repeated values mean separate printed numbers, not permission to use one occurrence repeatedly. Give each person or table two minutes on a card. Write a full expression rather than only saying the final result. Players may work together, split into independent pairs or solve quietly and compare afterwards.
An answer must pass two checks: it evaluates to 24 and uses exactly the card’s four numbers. For 1, 2, 3 and 4, the expression (1+2+3)×4 passes. The expression 6×4 does not pass even though it equals 24, because the card does not supply a 6 and three of its numbers have disappeared. Evaluate multiplication and division before addition unless brackets change the order.
For 2, 3, 4 and 6, one answer is 6×4×(3−2). For four fours, 4×4+4+4 works. For 2, 2, 3 and 3, use (3+3)×2×2. These are host examples, not mandatory expressions; accept any legal answer. Keep the answer page separate so a player who has not finished does not see it while collecting a fresh card.
After one minute, offer a hint such as “try making six before multiplying” without naming a player who seems behind. At the two-minute mark, the table may request the answer or move on. Stop after all four cards, then invite a different expression for a solved card. The first verified answer does not end another table’s thinking time. For younger groups, solve the first card together and leave the second pair of rounds optional; allow a calculator for checking while still requiring the full expression. Do not claim every arbitrary four-number set has a solution.
Preview before printing at 100% scale; turn off browser headers and footers. Keep host answers separate. This is a manual tabletop kit, not computer opposition or an automatic judge.
Use each of the four numbers once. + − × ÷ and brackets only; no joining digits, powers or division by zero.
Card 1 · 1 · 2 · 3 · 4
Card 2 · 2 · 3 · 4 · 6
Card 3 · 4 · 4 · 4 · 4
Card 4 · 2 · 2 · 3 · 3
| Card | Full expression | Uses all four? |
|---|---|---|
| 1 | ________________ | ____ |
| 2 | ________________ | ____ |
| 3 | ________________ | ____ |
| 4 | ________________ | ____ |
(1+2+3)×4 = 24
6×4×(3−2) = 24
4×4+4+4 = 24
(3+3)×2×2 = 24
Other legal expressions count. Evaluate and check the multiset of input numbers. First card may be demonstrated together.