How to play Greater Than

Play Greater Than

The rules

The grid is a square of 5×5, 6×6 or 7×7 cells. Fill every empty cell so that each digit from 1 up to the size of the grid appears exactly once in:

• every row;
• every column.

Some pairs of neighbouring cells have a sign between them. The point of the sign faces the smaller digit, and the open side faces the larger one. Every sign must be true.

Every puzzle has exactly one solution, and logic alone is enough to reach it. You never have to guess.

How to play here

• Select a cell: click it, or use the arrow keys.
• Enter a digit: the number keys, or the number pad below the grid.
• Notes (small candidates): press N or the Notes button. In notes mode, a digit you type is recorded as a small candidate. Shift + digit also writes a note.
• Erase: Delete, Backspace or 0.
• Undo and redo: Ctrl+Z and Ctrl+Y (on a Mac: ⌘Z and ⌘⇧Z).
• Hint: each press of Hint tells you more: first where to look, then which technique works there, and finally the digit itself. If there is a mistake on the board, the hint shows you where.

A digit that repeats in a row or column is marked with stripes and a wavy underline. A sign that is false is drawn in the error colour, and both of its cells are marked.

Difficulty levels

The level is set by the hardest technique the puzzle requires, not by the size of the grid:

Techniques

Full house

A row or column has one empty cell left. It takes the missing digit.

Sign next to a digit

A sign touches a cell that already holds a digit. If the empty neighbour must be smaller, remove every candidate equal to or larger than that digit. If it must be larger, remove every candidate equal to or smaller.

Hidden single and naked single

In a row or column, a digit fits in only one cell: it goes there. Or a cell has only one candidate left.

Sign bounds

Between two empty cells a < b, the smaller cell cannot hold the largest digit that b can still hold, or anything above it. The larger cell cannot hold the smallest digit that a can still hold, or anything below it. Follow chains: in a < b < c, the cell a can be at most n − 2.

Naked and hidden pairs

Two cells of a line with the same two candidates take those two digits: remove them from the rest of the line. Two digits that fit only the same two cells reserve them: remove every other candidate from those cells.

Naked and hidden triples

The same idea with three cells and three digits.

X-Wing

If a digit can appear in two rows only in the same two columns, remove it from every other cell of those two columns.

Tips

1. Start with chains of signs. A cell at the bottom of a long chain of < signs can only hold a small digit.
2. The largest digit can never sit on the small side of a sign, and 1 can never sit on the large side.
3. Write notes early: the sign techniques work on candidates, not only on placed digits.