Equation Builder · Strategy Guide
How to Beat Equation Builder
Four digits, four operators, one target — and a mental shortcut that always works.
The puzzle in a sentence
Equation Builder gives you four single-digit numbers and a target. Combine all four numbers using +, −, ×, and ÷ (each number used exactly once) to hit the target exactly. Your time is your score.
It's a direct descendant of the classic 24 Game, which has been used in competitive math classrooms for decades because it forces fast factoring and pattern recognition. The Minute Arcade version varies the target (not always 24) so the same numbers can demand different strategies each round.
Always start with factoring
The fastest path to any target is multiplication. Before you start trying combinations, glance at the target and ask: what are its factors? Then check whether your four digits contain a pair that multiplies to one of them.
If the target is 24 and you have a 6 and a 4, you're basically done — the other two numbers just need to combine to 1 (so they multiply or divide to themselves) and you can wedge them in. Common case: 6 × 4 × (5 ÷ 5) or 6 × 4 + (3 − 3).
Targets that are prime (29, 37, 41) or close-to-prime require additive strategies instead. Scan for two numbers that sum near the target and adjust.
Patterns to scan for
Most puzzles fall into one of a few recognisable shapes. Train your eye to spot these in 2-3 seconds.
- Target ± small number: if three of your digits combine to (target ± a small adjustment) and the fourth digit equals that adjustment, you're done.
- Multiply and add: large product plus a small remainder. Example: target 47, digits 8 7 5 6 → 8 × 5 + 7 = 47, then add 6 − 6 = 0... wait, you must use all four. So 8 × 5 + 7 × (6 ÷ 6)? No, that's 8×5 + 7×1 = 47. ✓
- Divide-then-multiply: when one digit is large and another divides it evenly, simplify first. 8 ÷ 2 = 4, then combine 4 with the remaining two.
- Distribute: factor out a common multiplier. (a + b) × c = a×c + b×c, useful when you have a × c already in mind.
A worked example
Target: 18. Digits: 3, 5, 7, 9.
Factoring scan: 18 = 2×9 or 3×6. You have a 9 and a 3, so 9 × 3 = 27 — over. 9 × (3 − x) for some x? 9 × 2 = 18, so you need (3 − 1) or (5 − 3)... but you can't reuse the 3. Try 9 × (5 − 7÷x)? Getting tangled.
Switch to additive: 18 = 9 + 9 (can't — only one 9), or 18 = 3 + 7 + something with 5 and 9 = 8. Need 5 and 9 to make 8. 9 − 5 ÷ 5 doesn't work — only one 5. So 9 − (5 ÷ 5) isn't available. Hmm.
Try multiply-and-add: 5 × 3 = 15, plus 9 − 7 = 2. Total 15 + 2 = 17. Close but no. 5 × 3 = 15, plus (9 + 7)/8... can't use 8.
Divide approach: 9 ÷ 3 = 3, then 3 × 5 + 7 = 22 — no. 9 ÷ 3 × 7 − 5 = 21 − 5 = 16 — no. (9 + 5) − (7 − 3) = 14 − 4 = 10 — no. (7 + 5 + 3 + 9 ÷ ...) — wait, just sum: 7 + 5 + 3 + 9 = 24. Subtract instead: 9 + 7 − 3 + 5 = 18. ✓ Done in five seconds.
The lesson: when factoring stalls, switch to additive scans before going deep. Most 4-digit puzzles have a clean additive path.
Common mistakes
Speed comes from skipping bad branches early.
- Trying every operation in order. You'll hit 1024 combinations. Scan factors first, then sums, then mixed.
- Forgetting the "use all four" rule. Easy to overlook the fourth number when the first three already work. The interface won't accept a partial answer.
- Going too deep on one approach. If you've been on a path for 15 seconds without convergence, abandon it and start over with a different first move.
Practice in your browser
Speed at this puzzle is purely about pattern recognition — and pattern recognition only comes from reps. Play five games in a row and your average time will drop noticeably. Equation Builder generates fresh number/target combinations each round.