Order of operations, without the confusion
Every Enigma puzzle is evaluated with the standard mathematical order of operations — the same rules taught as PEMDAS (US) or BODMAS (UK). Most lost attempts in the game come from one of two precedence mistakes. Here's how to never make them.
The two-tier rule
Forget the six-letter acronyms for a moment. For the operators that appear in Enigma there are only two tiers:
| Tier | Operators | When |
|---|---|---|
| 1 | × and ÷ | Resolved first, left to right |
| 2 | + and − | Resolved after, left to right |
That's the entire system. Parentheses, when they appear (level 4), simply create a sub-expression that is resolved — with the same two tiers — before anything outside it.
Mistake #1: adding before multiplying
The multiplication binds tighter: 3 × 4 happens first, then 2 + 12. In Enigma this matters constantly, because the equation template mixes tiers — [ _ ] + [ _ ] × [ _ ] means the last two slots form a unit. Read the template as chunks around the × and ÷ signs, not as a left-to-right story.
Mistake #2: forgetting left-to-right within a tier
Same-tier operators resolve strictly left to right: (10 − 3) + 2. The wrong answer, 5, comes from mentally grouping the tail as 3 + 2 first. The same applies to the first tier:
Exact division
Enigma only accepts divisions with no remainder. 7 ÷ 2 is never valid in a puzzle — the equation simply won't equal the target. Use this: when a template contains ÷, scan your number bank for pairs that divide cleanly and treat everything else as a decoy. It's one of the strongest filters in the strategy toolkit.
Parentheses (level 4)
A parenthesis promotes whatever is inside it to happen first — it's the only thing that outranks multiplication. When an Enigma template shows parentheses, the numbers inside them are the most influential slots in the puzzle: a difference of 1 inside the group is often a difference of 4 or 5 in the result.
A 10-second mental checklist
- Circle the × and ÷ first — compute those chunks.
- Then sweep once, left to right, through + and −.
- If there are parentheses, do them before anything, using the same two steps.
- Divisions must be exact — a remainder means a decoy is in the slot.
Run that checklist before pressing check and precedence will never cost you an attempt again.