Is every puzzle definitely solvable?

Yes, exactly rather than approximately. The tool runs an exhaustive search before offering the puzzle and discards any draw where the target cannot be reached. That matters because an unsolvable puzzle is indistinguishable from a hard one while you are working on it, and spending ten minutes on something impossible is the fastest way to stop enjoying this.

Do I have to use all six numbers?

No. Each number may be used at most once, and using fewer is entirely valid — often the neatest solutions use only three or four. Trying to force all six in is the most common reason a solvable puzzle feels stuck.

Why are fractions not allowed?

Because every intermediate result must be a positive whole number, which is the traditional rule. It keeps the puzzle mentally tractable — you can hold whole numbers in your head — and it happens to make an exhaustive search fast enough to run before every puzzle is shown.

How do more large numbers change the difficulty?

Generally they make it easier, because a large number multiplied by a small one lands near a three-digit target in one step. Six small numbers is the hardest setting: reaching three figures from values of ten or less usually needs two intermediate results multiplied together.

Is this a television game?

The mechanic — reach a target from drawn numbers using each at most once — is a generic arithmetic puzzle used in classrooms long before and quite independently of any broadcast version. Nothing here reproduces any programme's format, branding, presentation or rules text, and this site is not affiliated with any.

Number Target Challenge Generator

Six numbers, a three-digit target, and the four operations — get as close as you can using each number at most once. It is the best mental-arithmetic exercise there is, because it rewards flexibility rather than recall. Every puzzle here is guaranteed solvable exactly, because the tool solves it before offering it and discards any draw it cannot.

Large numbers

How many of the six come from 25, 50, 75, 100. Zero is the hardest setting.

Seed (optional)

Reproduces a puzzle, so a class can all work on the same one.

Lowest target

Between 100 and 999.

Highest target

A narrower range makes the difficulty more consistent.

Your numbers and target will appear here.

What this generator does

Draws six numbers and a target between 100 and 999, and guarantees the target can be reached exactly. That guarantee is the product: a puzzle where the target happens to be unreachable is indistinguishable, while you are working on it, from one you simply have not cracked, and it is deeply demoralising. The tool searches exhaustively for a solution before offering the puzzle, keeps that solution, and shows it when you ask.

How to use this tool

Choose how many large numbers to include — more large numbers usually makes it easier.
Press Generate for six numbers and a target.
Reach the target using each number at most once, with +, −, × and ÷.
Reveal a worked solution when you are done, or stuck.

Understanding the controls

Large numbers: How many of the six are drawn from 25, 50, 75 and 100 rather than from 1 to 10. More large numbers generally makes a three-digit target easier to reach, because you can get near it with one multiplication. Zero large numbers is the hardest setting and produces the most elegant solutions.
Target range: Between 100 and 999. A narrower range makes the difficulty more consistent, which matters when you are setting the same puzzle for a class; the full range varies a lot from one draw to the next.
Seed: Reproduces a puzzle exactly, so a class can all work on the same one or you can come back to a hard one later.

Worked examples

A typical draw: 100, 25, 6, 2, 3, 4 with a target of 752. One route: 100 + 25 = 125, 125 × 6 = 750, 750 + 2 = 752.
Using fewer numbers: A solution that uses four of the six is entirely valid and often more elegant than one using all of them.
Why whole numbers only: 100 ÷ 3 is not allowed as an intermediate step. It is the traditional rule and it is also what keeps the puzzle mentally tractable.
The hardest setting: Zero large numbers means six values from 1 to 10 reaching a three-digit target, which almost always needs a multiplication of two intermediate results.

Common use cases

Mental arithmetic practice that adults find genuinely engaging
A maths lesson starter that scales from primary to adult without changing
Family games in the car or over dinner, needing nothing but the numbers
Building fluency with factors, which is what the good solutions rely on
Numeracy revision where drill sheets have stopped working

How this generator works

The solver works on the six numbers as a collection, repeatedly replacing any two of them with the result of an operation between them. That covers every possible way of bracketing an expression without having to enumerate expressions at all, which is what makes an exhaustive search feasible. Intermediate results are constrained to positive whole numbers — the rule the game is played under — and that constraint also prunes the search enough to finish in milliseconds. If no solution exists for a draw, the draw is discarded and another is made, so an unsolvable puzzle is never shown.

Randomness and fairness

The six numbers and the target are drawn with the browser's cryptographic random number generator, and then the puzzle is *checked* rather than trusted: the solver runs before the puzzle is shown, and an unsolvable draw is discarded and redrawn. So the numbers are random and the solvability is not — it is a guarantee. A seed reproduces a puzzle with a deterministic, non-cryptographic generator, which is what lets a whole class work on the same draw.

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

Assumptions this tool makes

Each drawn number may be used at most once, and does not have to be used at all.
Every intermediate result must be a positive whole number.

Limitations and good to know

Only the four basic operations. No powers, no roots, no concatenating digits, no factorials — all of which appear in variants and none of which are allowed here.
Intermediate results must be positive whole numbers, so no fractions and no negatives at any stage.
The solution shown is one solution, not the shortest or the most elegant. Most puzzles have many, and yours may be better.
It does not check your answer. It gives you a correct one to compare against.
There is no timer or scoring. Thirty seconds is the traditional limit and a phone does it better than this page would.

Common mistakes

Trying to use all six numbers: You do not have to. Many of the best solutions use four, and insisting on all six is the most common reason a solvable puzzle feels impossible.
Working forwards from the numbers: Work backwards from the target instead. Look for factors of the target, or of a number close to it, among the six — that is how experienced solvers actually approach it.
Ignoring subtraction as a way to adjust: Getting near the target with a multiplication and correcting with a small subtraction is the single most productive pattern in the game.
Giving up when a route produces a fraction: Division is only legal when it comes out whole, so a fractional result means that route is closed rather than that you are stuck. Back up one step and try a different pairing.

Practical tips

Say the target's factors out loud before doing anything else. If 7 divides it and there is a 7 in the six numbers, you are most of the way there.
For a class, use a seed so everybody has the identical puzzle and the comparison of methods afterwards is meaningful.
Zero large numbers is the setting for a group that has got good at it. It is noticeably harder and the solutions are far more interesting.

Troubleshooting

I cannot get anywhere near it: Look for a multiplication that lands within about twenty-five of the target and then adjust with what is left. Almost every solution has that shape.
The revealed solution is not the one I found: Most puzzles have many solutions and the tool shows the first one its search reached. If yours reaches the target legally it is equally correct, and possibly shorter.

Privacy and your data

Nothing is entered and nothing is stored. Puzzles are generated in your browser, nothing is uploaded or written into the page address, and analytics records only that the tool was used along with how many large numbers were chosen — never a puzzle or a solution.

Frequently asked questions

Is every puzzle definitely solvable?: Yes, exactly rather than approximately. The tool runs an exhaustive search before offering the puzzle and discards any draw where the target cannot be reached. That matters because an unsolvable puzzle is indistinguishable from a hard one while you are working on it, and spending ten minutes on something impossible is the fastest way to stop enjoying this.
Do I have to use all six numbers?: No. Each number may be used at most once, and using fewer is entirely valid — often the neatest solutions use only three or four. Trying to force all six in is the most common reason a solvable puzzle feels stuck.
Why are fractions not allowed?: Because every intermediate result must be a positive whole number, which is the traditional rule. It keeps the puzzle mentally tractable — you can hold whole numbers in your head — and it happens to make an exhaustive search fast enough to run before every puzzle is shown.
How do more large numbers change the difficulty?: Generally they make it easier, because a large number multiplied by a small one lands near a three-digit target in one step. Six small numbers is the hardest setting: reaching three figures from values of ten or less usually needs two intermediate results multiplied together.
Is this a television game?: The mechanic — reach a target from drawn numbers using each at most once — is a generic arithmetic puzzle used in classrooms long before and quite independently of any broadcast version. Nothing here reproduces any programme's format, branding, presentation or rules text, and this site is not affiliated with any.