Why is division not offered?

Because it produces fractions almost immediately, and a chain that only works with a non-integer partway through is a much less satisfying puzzle to solve by hand.

Are there always exactly one answer?

Yes. Every combination is evaluated during generation, and a candidate with two or more solutions is thrown away before you ever see it.

How is this different from the number target challenge?

That one gives you numbers and asks you to reach a target using any arithmetic you like. This one fixes both the numbers and their order, and asks only which signs go in the gaps.

Missing Operator Puzzle Generator

This is a cryptarithm turned inside out. There, the operations are visible and the values are hidden; here the values are given and you have to work out the signs. Because multiplication is worked out before addition and subtraction, the answer depends on precedence as much as on arithmetic, which is exactly what makes it a useful exercise. Every puzzle is checked to have precisely one solution before it appears.

How many numbers

Between 3 and 6. More numbers means more gaps to fill and a harder search.

Seed (optional)

A word brings the same puzzle back, so a class can all work on it.

Your puzzle will appear here.

What this generator does

Produces a chain of numbers and a target, with the operators blanked out. Every possible combination of plus, minus and times is evaluated under ordinary precedence, and the puzzle is only offered if exactly one of them hits the target. Puzzles with several answers are discarded, because a puzzle where two different sign patterns both work has no correct answer to mark.

How to use this tool

Choose how many numbers you want in the chain.
Press make a puzzle. Each gap holds a plus, a minus or a times.
Work out the one combination that reaches the target.
Reveal the answer, or seed the puzzle to share it.

Understanding the controls

How many numbers: Between 3 and 6, which means two to five gaps. Each extra gap multiplies the search space by three, and makes a unique answer rarer — so longer puzzles take a few more attempts to find.
Seed: Reproduces the same puzzle exactly, which is what a shared worksheet needs.
Show the answer: Fills the signs in. It is the combination the puzzle was built from and the only one that works.

Common use cases

Practising order of operations in a form that rewards understanding rather than recall
A quick numeracy starter with a single defensible answer
Homework that can be regenerated identically from a seed
Showing why 2 + 3 x 4 is not 20, using a puzzle rather than a rule
A mental arithmetic warm-up that scales with the number of gaps

How this generator works

A random chain of numbers and operators is generated and evaluated to give a target. Then every operator combination is tried against that target, with multiplication collapsed before addition and subtraction so precedence is handled correctly. If more than one combination reaches the target, the candidate is thrown away and another is tried. Targets are also kept within a range a person would actually attempt, so a puzzle never resolves to something in the tens of thousands.

Randomness and fairness

The numbers and the hidden operators are random. Without a seed this uses the browser's cryptographically secure generator; with a seed a small deterministic one, which is reproducible and therefore explicitly not cryptographically secure.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

Multiplication is evaluated before addition and subtraction.
Operations of equal precedence are evaluated left to right.

Limitations and good to know

Only plus, minus and times. Division is excluded because it produces fractions that make most chains unsolvable in whole numbers.
No brackets. The puzzle is about precedence as it stands, not about inserting grouping.
Difficulty is not graded beyond the number of gaps.
Nothing persists between visits — seed anything you want back.

Common mistakes

Working strictly left to right: Multiplication binds tighter. 2 + 3 x 4 is 14, not 20, and most wrong answers here come from that one step.
Stopping at the first combination that works: There is only one, so if you have found a second, one of them has been evaluated with the wrong precedence.
Assuming a large target means multiplication everywhere: A single multiplication in the right place often gets further than several in the wrong ones.

Practical tips

Estimate first: if the target is far larger than the sum of the numbers, at least one gap must be a times.
Try the largest pair of adjacent numbers as a multiplication and see whether the remainder is reachable.
For a class, three numbers is a genuine warm-up and five is a real challenge — the jump is steeper than it looks.

Privacy and your data

Everything is generated in your browser. No puzzle, seed or answer is transmitted or stored between visits.

Frequently asked questions

Why is division not offered?: Because it produces fractions almost immediately, and a chain that only works with a non-integer partway through is a much less satisfying puzzle to solve by hand.
Are there always exactly one answer?: Yes. Every combination is evaluated during generation, and a candidate with two or more solutions is thrown away before you ever see it.
How is this different from the number target challenge?: That one gives you numbers and asks you to reach a target using any arithmetic you like. This one fixes both the numbers and their order, and asks only which signs go in the gaps.