Operator Inference
Find the missing + − × ÷
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What is the Operator Inference?
An operator inference puzzle shows an equation with the operation signs removed, such as 6 ? 4 = 24, and asks which of +, −, × or ÷ belongs in the gap. Instead of calculating a result, you reason backwards from the numbers to the relationship that links them. Puzzles of this kind are a familiar feature of numerical reasoning tests and puzzle books.
Working out the missing operation is a form of inductive reasoning about numbers: you test possible relationships and keep the one that fits. With more than one gap, you also need the order of operations, where × and ÷ are applied before + and −. The Neuroptimize Operator Inference game builds each puzzle so that exactly one choice of operators makes the equation true.
How to play the Operator Inference
- An equation appears with a dashed box in place of each missing operator, and the result shown on the right. You have 60 seconds to solve as many as you can.
- Tap the operator button that makes the equation true. On a keyboard you can type + and - for plus and minus, * or x for ×, and / for ÷.
- At the start only + and − are offered. × joins from level 4, and ÷ from level 7.
- From level 12 there are two gaps, and from level 24 there are three. Fill them from left to right, and use Undo or Backspace to change your last pick before the final gap is filled.
- The equation is checked when every gap is filled. If any operator is wrong, it counts as a mistake and the correct equation is shown.
- Multi-operator puzzles follow the standard order of operations, so × and ÷ are worked out before + and −. Puzzles with more gaps are worth more points.
Strategies and tips
Compare the result size
Look at whether the result is bigger or smaller than the numbers. For 9 ? 7 = 63, the result is far larger than both, which points to ×. For 48 ? 6 = 8, the result is smaller than the first number, so try − or ÷.
Check the last digit
For 27 ? 14 = 41, 7 + 4 ends in 1, which matches, while 7 − 4 ends in 3. The last digit often rules out + or − without a full calculation. For ×, the last digit of the result comes from multiplying the last digits.
Group the × and ÷ first
With several gaps, remember that × and ÷ bind tighter than + and −. In 3 ? 4 ? 2 = 14, trying × then + gives 12 + 2 = 14. Think of each multiplication as a single block, then add or subtract the blocks.
Use division as a clue
Every division in these puzzles comes out exactly. If one number divides neatly into the one before it, ÷ is a real possibility. If it does not divide evenly, you can rule ÷ out for that gap straight away.
Work from the result backwards
In three-gap puzzles, look at how far the result is from the biggest product you could make. If 5 × 6 = 30 and the result is 27, the rest of the equation must take away 3. Narrowing the options this way beats trying every combination.
The science behind the Operator Inference
Identifying the operation that links a set of numbers is a form of inductive reasoning about numerical relationships. When more than one operation is involved, it also depends on knowledge of the order of operations.
Frequently asked questions
Can there be more than one correct answer?
No. Each puzzle is checked when it is created so that only one combination of the available operators makes the equation true. That lets the game mark your answer as simply right or wrong.
What order of operations does the game use?
Multiplication and division are worked out before addition and subtraction, and operations of the same kind go left to right. This is the standard rule taught in schools, sometimes remembered as BODMAS or BIDMAS in the UK and PEMDAS in the US.
Can I change an operator after picking it?
Yes, in puzzles with more than one gap. Tap Undo, or press Backspace on a keyboard, to remove your last pick. Once the final gap is filled, the answer is checked straight away.
Is Operator Inference free?
Operator Inference is a Pro game in Neuroptimize, and Pro starts with a 7-day free trial. Free players can also get it as the Pro game of the day in their daily workout.