Skip one square, and write the three pairs down

Six faces, three pairs, every time

That is the foundation, and it is worth saying as a fact rather than a technique: every net you will ever see gives you exactly three pairs of opposite faces. No more, no fewer.

You can only ever see three faces of a cube at once, and they always meet at one corner.

Skip one

Squares that touch share an edge, so they fold up side by side. Never opposite.

Which gives the rule: skip one square along a straight line, and those two faces are opposite.

It is the most useful fact in the topic. It also has a natural limit, and the people who write the papers know exactly what it is.

When the net bends

The skip-one rule is easy on a straight row of four. So at the top end of the paper, they stop giving you straight rows.

You get staircases. You get zig-zags. Nets with no line of four anywhere.

So look for a zig-zag instead: along a bit, turn, and then turn back the other way. The two ends of that zig-zag are opposite.

And always finish with the leftover check: there are exactly three pairs, so once you have two of them, the two squares left over are the third. On a staircase net that does half the work for you.

Write the pairs in the margin

Before looking at the options at all, write the three pairs down. It takes about eight seconds and it saves thirty.

Then eliminate — any cube showing two faces that are a pair cannot exist.

And if two options survive, compare them face by face against each other. Do not go back to the net and start again; restarting is what eats the time.

The mirror trap

This is what separates a good mark from a great one.

The examiner shows a cube with all three of the right faces on it. None of them is a pair, so the elimination check passes it quite happily.

But the three faces are in the wrong order round the corner. It is the mirror image of the real cube, and it cannot exist.

So once the pair check has left you with one or two options, stop eliminating and switch checks: go round the corner in the same direction on both cubes and compare the order.

Which way up?

And one layer beyond that. Up to here we have only asked which faces are visible and where. At the top of the paper, the question also cares which way up they are.

Same three faces, same three places, and the letter turned a quarter turn — that cube cannot exist either.

This is why arrows, letters and stripes turn up so often in the hard questions. They are the shapes where turning shows. A circle turned round still looks like a circle, so it cannot trap anybody.

So the checks run: right face, right place, right way up.

How can we practise this at home?

A cereal box, cut open, is a net. Better still, cut six squares of card, tape them into a net, fold it, and mark the pairs — the moment a child sees two squares they expected to be opposite folding up side by side is worth more than an explanation.

Then the quick drill, no equipment: draw a net, and ask only for the three pairs. Not which cube, not which option. Just the pairs. That is the part the exam actually tests.