Grid logic

Before you read anything, look at this for 20 seconds and decide what goes in the empty cell.

Don't worry about being right. Guessing first makes the rest of the chapter stick. If you'd rather just be told the rule, skip ahead. No problem.

What you probably noticed: the same few shapes appear again and again, but never twice in the same row, and never twice in the same column. That noticing is the whole skill. By the end of this chapter you'll spot a Latin square the moment a matrix opens.

Latin square: each value appears exactly once in every row and exactly once in every column.

It is the signature mechanic of real matrix tests. The grid uses a small set of values — usually three shapes, or three colours, or three sizes. Each row holds all three, once each. Each column holds all three, once each. Nothing repeats inside a line.

The canonical Latin square: three shapes, each appearing once per row and once per column.

A small set of values — almost always three. You can list them on one hand: circle, square, triangle. Or red, blue, green. Or small, medium, large.

The work is not what the values are. The work is which attribute is Latin, and whether more than one attribute is Latin at the same time:

• Single Latin — one attribute (say, shape) follows the rule. The others are decoration.
• Two-attribute Latin — shape and colour both follow the rule, independently. You solve two Latin squares in the same grid.
• Cayley table — the pair (shape, colour) is unique across all nine cells, not just each attribute on its own.
• Inner Latin — the rule lives on a small shape inside each tile, not on the tile itself.

You'll recognise the family fast: a short list of values, no line repeating. Naming which attribute carries the rule takes a few more seconds.