How to reach the target in Number Forge

A handful of numbers, four operations, and a target. Use each number at most once.

The instinct is to combine numbers forwards and see where you land. Working backwards from the target is far more effective.

Work backwards

Ask what would produce the target. If it is 528, notice that 528 is 500 plus 28, or 24 times 22, or 530 minus 2. Each of those is a smaller problem, and you can check straight away whether your numbers can produce the pieces.

Factorising is especially productive with large targets. If the target divides neatly by one of your numbers, you have reduced the problem substantially in one step.

Build the big number first

Multiplication moves you furthest, so get near the target with a product, then adjust with addition and subtraction. Trying to add your way up from small numbers wastes the large ones.

Division is worth checking early

People underuse division because it rarely comes out whole. But when it does it is powerful, and it is quick to check: scan your numbers for a pair where one divides the other.

Near misses count for something

If you cannot hit the target exactly, get as close as you can — being two away is a much better outcome than abandoning the round. And often the near miss reveals the exact answer: if you are three off and have an unused 3, you are finished.

Keep track of what you have spent

Each number can be used once. The commonest mistake in a hurry is a solution that reuses one. Say the numbers out loud as you consume them.

Frequently asked questions

Do I have to use every number?

No. Each may be used at most once, and unused numbers cost nothing.

Are intermediate results allowed to be fractions or negatives?

Stick to whole positive results as you go. Aiming for clean intermediates keeps the arithmetic checkable and is how these puzzles are intended to work.

Is every target reachable?

Every round has at least one exact solution. If you cannot find it, getting close still scores.