Cube Views

Three drawings show the same cube from three angles. Its six faces carry six different symbols. One face has been left blank, and the tiles you choose from are six different symbols too — so the whole question is which face the gap is.

These come from published practice books, not an exam board's own booklet. They are still worth doing. They turn on the same fact as the cube-net questions.

And here is that fact. The symbol you need is already on the page. The blank face is drawn, symbol and all, in one of the other two pictures. All seventeen of our exam-level questions do this. So never cross a symbol off for being visible. Seeing it is how you find it.

The method

Five beats: name the two neighbours, find the pair that never meet, pin two drawings together, read round the shared face, then name the face and say its symbol.

1. Name the two neighbours. The drawing with the gap shows two other symbols. Both of them sit next to the blank face, so neither can be the answer. That is one tile gone before you have thought about anything.
2. Find the pair that never meet. Look for two symbols that never once appear in the same drawing. Those two are back to back on the cube, and back-to-back faces are never in view together. When one of them turns out to be the gap, the other is the trap — and it is on the card every single time.
3. Pin two drawings together. Find a face that two drawings both show. That shared face is the hinge: the cube has been turned about it, and everything else follows.
4. Read round the shared face. Four faces sit in a ring around any face you pin. Read that ring off the first drawing, read it off the gap drawing, and see how far it has slid.
5. Name the face, then say its symbol. Slide the ring back to where the gap is and you have named the face. Only then read what sits on it.

Beat 2 is the one worth a name: the pair that never meet. It is the only cut you can make without turning the cube at all.

Give each question 30 to 35 seconds.

Worked example

Three drawings of one cube. In the third, one face is blank. Then five tiles, each showing a different symbol. The drawings show one cube. All six faces are different. Which symbol belongs on the blank face?

1. Name the two neighbours. In the drawing with the gap, S is on top and J is on the right. Both touch the blank face. J is one of the tiles — cross it out.
2. Find the pair that never meet. C appears only in the first drawing and N only in the second. They never share a picture, so they are back to back.
3. Pin two drawings together. J is on the right in the first drawing and on the right in the gap drawing, so the cube has been turned about J and nothing else.
4. Read round the shared face. The four faces around J run C, F, N, S and back to C. In the first drawing C is on top; in the gap drawing S is on top. S comes one place before C, so the whole ring has slid back by one.
5. Name the face, then say its symbol. F was on the left. Slide back one and the face on the left is C. So C belongs in the gap — and N, the symbol back to back with it, is the trap sitting right there on the card.

Answer: C

Rules to watch

• Only one drawing shows the face you need. On every exam-level question the blank face is on show in exactly one of the other two pictures. Find that picture and you have found the answer.
• Three faces at a time. Never four, never two opposite ones. Any two faces you can see in one drawing are next to each other on the cube.
• The two symbols beside the gap are never the answer. They are its neighbours. One of them is on the card on every exam-level question, and crossing it out is free.
• A symbol you can see elsewhere is not ruled out. The drawing that shows the covered face is showing this face. Beat 1 only rules out the two symbols drawn in the same picture as the gap.
• Where a face is drawn is not which face it is. A gap on the left is not "the left face". Follow the face between drawings; never read the position on the page.
• The turn does not matter any more. Every tile is printed the right way up, so a symbol lying on its side in a drawing is still that symbol. Read what it is, not how it sits.

Watch for these traps

This type builds only two kinds of wrong answer, and every exam-level question carries both.

• The face back to back with the gap. 17 of the 68 wrong tiles — exactly one on every question. It really is on the cube, and it is the one symbol that can never be seen beside the blank face. Beat 2 kills it without any turning.
• A face next door to the gap. 51 of the 68 — three on every question. These are the real work. 17 of them are drawn beside the gap, so beat 1 removes one per question for nothing; the other 34 are neighbours you cannot see from the gap drawing, and those have to be reasoned about.

Stuck at 30 seconds? Cross out the two symbols drawn beside the gap and the one that never shares a picture with your best guess. Two gone out of five, and it costs nothing.

Try these yourself

Now have a go yourself — tap the face that belongs there.

Related

• The complete 11+ question-type guide
• Cubes and Nets — the same opposite-face rule, folded up
• Different Views — one solid seen from another side

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.