Grids and matrices

The row and the column that cross at the question mark

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

The whySix 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

HintSameness, not movement, is what a row shows you.

The whyRows 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

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

The whySay 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

HintHalf right is still wrong — test against both directions.

The whyThe 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

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

The whyComparing 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

HintNine boxes, and one of them stands empty.

The whyEvery 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

HintThe pattern jumps over the point next door.

The whySix 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

HintHalf of six.

The whyEach 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

HintA single rule, repeated all the way round.

The whyThat 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

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

The whyOnly 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

HintAn untouched copy ignores the very rule the pair demonstrates.

The whyA 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

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

The whySame 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.