Number Grid

A free deductive reasoning game: fill a small number grid by checking each row, column and box until every square has its one possible answer.

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Fill every square so each row, column and box holds each number once. Tap a square, then tap a number.

New to this game? Try the short tutorial.

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Tutorial Practise

About this game

Number Grid uses deductive reasoning in a constraint satisfaction puzzle. A constraint is simply a rule an answer must obey: here, each number appears once per row, column and box. The classic task family is grid filling by elimination. Constraint satisfaction gives a framework for checking which choices can fit together. Every generated puzzle has one answer, and our solver checks that it can be reached by reasoning without guessing.

Your scores in this game combine your grid completion rate with the difficulty reached through the game’s adjustments. Every square must be filled correctly. Wrong placements are rejected and counted; too many end the grid. Later levels add deadlines, but faster placement adds no bonus. Track results within your age band using the same rules. These scores describe completing Number Grid puzzles, without measuring your arithmetic or success at other puzzles.

How to play

Select an empty square and check its row, column and box.
Choose a number that can fit all three groups.
Keep filling squares until every row, column and box contains each number once.
Use Erase to remove a placed number if you want to reconsider it.

Tips

Start with a row, column or box that has only one missing number.
For each candidate, check all three groups before placing it.
If two squares share the same two possible numbers in a group, consider what that excludes elsewhere.

How it adapts

Kids, teens and adults have different level ceilings, and completed grids increase the challenge within their band. Four-by-four grids grow into six-by-six grids with more blanks and harder deductions, while puzzle deadlines begin at level four.

Questions

Do Number Grid puzzles need guessing?

No. Each generated grid is checked for exactly one answer and for a reasoning path using the techniques allowed at its level. Look for exclusions and forced placements before putting a number into a square.

Do I need arithmetic to fill the grid?

You do not add or multiply the numbers. They act as labels that must not repeat in each group. Four-by-four grids use one through four; six-by-six grids use one through six.

What happens after a wrong placement?

The number is rejected, and you can try again while mistakes remain within the allowance. A four-by-four grid allows two mistakes and a six-by-six grid allows three; the next mistake ends that grid.

The research behind it

Mackworth introduced arc-consistency methods for constraint networks. Browne studied how logical deductions can solve puzzles step by step. Both are papers about solving methods; neither studied Number Grid players or shows that these puzzles improve abilities elsewhere.