Cubes and Nets

A flat net is shown with a symbol on each of its six panels. You pick the cube it folds up into.

Some run the other way. Here is the cube — which net makes it? Seven of our twenty-seven exam-level questions are that kind.

Not every net is a cross. Ours run 11 crosses, 9 zigzags and 7 tees. So 16 of the 27 are some other shape. The trick most books teach only works on a cross.

The method

Five beats: mark the three pairs, cross out the impossible cube, read the corner, check the turns and say the whole answer, turn it round.

1. Mark the three pairs. Find the three sets of two panels that end up back to back. Two rules do most of it. In any straight run of three panels, the two ends are back to back. Two panels that share an edge never are. A zigzag has no straight run of three. There you roll the net along, one panel at a time.
2. Cross out the impossible cube. No cube ever shows two back-to-back faces at once. So a cube showing both halves of a pair cannot exist. There is one on every forward question, and it is free.
3. Read the corner. Take the three symbols on a cube. Read them clockwise round the corner where they meet. Now work the same three out from the net. A cube that reads the other way round is a mirror, and no folding makes one.
4. Check the turns and say the whole answer. Right symbols in the right places is not enough — one may be a quarter turn out. A symbol's way up on the net is not its way up on the cube. Then say it whole: which symbol is on top, which way up, and which of the other two is on the left.
5. Turn it round. Backwards questions only. All five nets share one shape on purpose, so shape tells you nothing. Pick a clear symbol on the cube. Find it on each net, and ask what has to sit next to it.

Beat 3 is the one worth a name: the corner read. It decides Cube Views too, and nothing else separates a cube from its mirror.

Give each question 30 to 40 seconds. If you may write on the paper, draw a line joining each pair. It is the most useful pencil mark here.

Rules to watch

• The touching rule runs one way only. Two panels that share an edge on the net are next to each other on the cube. The other way round is false. Faces showing together need not touch on the net. On all 20 forward questions, the three symbols on the right cube fail to all touch. So "they must touch" throws the answer out 20 times out of 20.
• Getting the pairs right does not prove the cube. A mirror keeps all three pairs exactly as they should be. The pairs remove one cube; beat 3 does the rest.
• Do not pick by "these two look alike". Two cubes really are mirrors of each other. That is easy to spot. But the harder questions carry two such pairs, so it tells you nothing.
• Which way up counts on some symbols, not others. A circle, a square or a plus looks the same however you turn it. So a turning trap has to live on a letter, an arrow or a triangle. Check those first.

Watch for these traps

We looked at every wrong option in our twenty-seven exam-level questions.

• The mirror image. 40 of the 108, the biggest group, and two on every forward question. Every symbol is on a face it belongs on. Every pair is right. Only left and right are swapped, and no folding does that. Read the three symbols round the corner and check the order, not just which ones are there.
• Two back-to-back faces on one cube. 34 of the 108. One on every forward question, two on every backwards one. It looks reasonable, because the symbols really are all on the net. It is the combination that cannot exist. Hunt it first: it is the cheapest cut you will get.
• The right symbol at the wrong turn. 34 of the 108. Everything correct except one face turned a quarter or a half. The backwards questions carry two of these and no mirror at all, so turns matter most there.

Stuck at 30 seconds? Cross out the back-to-back cube, then any cube with symbols plainly in the wrong places, then choose. Do not spend the time on turns — positions decide more often.

Try these yourself

Now have a go yourself — tap the cube that the net makes.

Related

• The complete 11+ question-type guide
• Shaded Nets — the same folding, with colours and other solids
• Cube Views — the same corner read, without a net

All example questions come from the Brainblox question bank — practise this question type inside 15 arcade games, timed mock exams and focused practice. Brainblox is an independent app: not affiliated with, endorsed by or licensed by any exam board, school or assessment publisher, and it contains no past papers.