Grids and matrices

The row and the column that cross at the question mark

提示Trace sideways and downwards from the gap; the rest of the grid can wait.

为什么Six of the eight drawn cells have nothing to say about the gap. Narrowing your eyes to the two lines that meet there turns a busy picture into two small, simple patterns.

Holds it steady while everything else changes

提示Sameness, not movement, is what a row shows you.

为什么Rows and columns in these puzzles usually work by keeping something constant rather than by transforming it step by step. If nothing in a row seems to stay put, you are probably watching the wrong feature.

Work out the row rule and the column rule one at a time

提示Do not try to hold both directions in your head at once.

为什么Say the first reading out loud to yourself before you start the second. Two half-held patterns blur together far more easily than two settled ones.

It obeys one of the two rules but not the other

提示Half right is still wrong — test against both directions.

为什么The options are built as near misses on purpose: right shape with the wrong shading, right shading with the wrong shape. Whichever reading you did first is the one the trap will satisfy.

Slide it into the gap and see if both lines still work

提示Do not judge it beside the other options — judge it where it would sit.

为什么Comparing options against each other is a different job from testing one against the puzzle. The second job is the one that finds a mistake.

8

提示Nine boxes, and one of them stands empty.

为什么Every one of those drawn cells is evidence, but only the ones sharing a line with the gap are evidence about the answer.

Neighbours belong to different families, so they need not match

提示The pattern jumps over the point next door.

为什么Six points on a star hold two designs taking turns, so side-by-side points are meant to differ. Reading them as a single sequence is the commonest way to go wrong on this layout.

3

提示Half of six.

为什么Each family sits on the corners of a triangle hidden inside the star, and every point of one family carries the same design — so the two you can still see hand you the missing one.

Just one, and it is applied to every corner

提示A single rule, repeated all the way round.

为什么That is what makes the two triangles "similar": one uniform move, not a fresh idea at each corner. If your reading needs two different moves, it is the reading that is wrong.

From a pair whose corners are both still drawn

提示Two of the matching couples are complete — the rule shows itself there.

为什么Only one corner is missing, so the other pairs are worked examples. Find the move on a complete pair, then carry it across to the corner whose partner is blank.

No — the change has not been made to it

提示An untouched copy ignores the very rule the pair demonstrates.

为什么A plain copy is planted in almost every one of these questions, because it looks reassuringly familiar. The answer always shows the move; the copy shows you skipped it.

cell and point

提示One layout is a table of boxes; the other has six arms.

为什么Same habit, two pictures: find the group the gap belongs to, read the group, then fill the gap. Knowing which word goes with which layout keeps the two methods from tangling.