Futoshiki Puzzle

Sudoku with the boxes replaced by signs

Fill a 5×5 grid so each row and each column carries the digits 1 to 5 exactly once. Between some adjacent pairs of cells sits a < or a >, and every one of them has to hold.

Futoshiki means inequality in Japanese, which is the whole puzzle in one word. The grid is small enough that a beginner can learn the rules and finish a puzzle in the same sitting, and the signs give a great deal of information away, so it is a much gentler entry point than a 9×9 anything.

One to eight puzzles a page, four by default.

Reading the signs

• A < between two cells means the left or upper one is smaller.
• A > means the opposite.
• Some cells start with a digit already printed, and some grids give you nothing at all and rely on the inequalities to carry the entire deduction.
• Every sign must hold in the finished grid, without exception.

That last point is what makes the puzzle work: an inequality is not a hint that might help, it is a constraint that eliminates. A single > rules out four of the twenty-five possible digit pairs before you have written anything.

Where to start on a fresh grid

Extremes first. A cell with signs pointing into it from both sides is the smallest in its line, and a cell with signs pointing away from it on both sides is the largest. Those are free.

Then chains. Three cells reading a < b < c must take three distinct increasing digits, which is a much stronger constraint than it looks: if a 2 is already placed elsewhere in that row, only 1, 3, 4 and 5 remain, and the increasing order leaves exactly four possible triples. Add one more given, say a 4 in the c cell, and it collapses to one.

Then Latin-square logic, which never stops applying: each digit exactly once per row and column, regardless of what the signs say.

Why it feels different from other grid puzzles

Most logic puzzles ask you to reason within a structure. Futoshiki asks you to combine a local clue, which is a relationship between exactly two cells, with a global rule about the whole line, and few other puzzles demand precisely that pairing.

The result is that information radiates. Place one digit and a chain of inequalities carries the consequence three cells away, which produces the one-move-unlocks-three feeling that good logic puzzles run on and this one delivers in a very small space.

Printing a set

Choose how many puzzles per sheet and whether to include the solutions page. Enter a seed if you want the same set again later, or leave it blank for something new each time.

Six to a page keeps the cells large enough to write digits in without crowding the signs between them, and eight is tight. Print at full scale on A4 or US Letter. There is no language content anywhere on the sheet, which makes it usable in any classroom and a fair puzzle for a child who finds word puzzles hard going.