How does the cube net test work?
Each puzzle shows a net: six squares joined edge to edge, each with a symbol, that fold up into a cube with the symbols on the outside. Below it are 4 cubes, each showing three faces around one corner. Only one of them can be made from the net; pick it. There are 8 puzzles, each with a new net or a new arrangement of symbols.
The symbols look the same however a face is turned, so a cube can only be told apart by which faces sit next to each other and which way round they go. The wrong cubes are impossible ones: a corner showing two faces that end up opposite, or the mirror image of a real corner. The site's tests check every puzzle has exactly one possible cube.
How many nets does a cube have?
11. There are 35 ways to join six squares edge to edge, and exactly 11 of them fold into a cube. The ones used here were found by folding all 35 by computer, and the site's tests fold each again to check it closes into six different faces. Every puzzle uses one of them, turned so it is at least as wide as it is tall.
How do you tell which cube a net makes?
Use two checks. First, opposite faces are never seen together: in a straight row of three squares on the net, the first and the third end up opposite, so any cube showing both is wrong. Second, check the order around the corner: a cube with the right three faces going round the wrong way is a mirror image, and no folding makes it.
- Find the opposite pairs. Mark the three pairs on the net before you look at the cubes.
- Pick a face and go clockwise. On the net, note which faces surround it in order; on the cube, the same faces must follow each other the same way round.
- Fold one flap at a time. Keep one square as the base and lift its neighbours in your head, rather than picturing the whole cube at once.
Where are cube net questions used?
In tests of spatial ability. The Educational Testing Service's Kit of Factor-Referenced Cognitive Tests (1976 edition) includes a Surface Development Test, of picturing a flat shape folded into a solid, and a Cube Comparisons Test, of deciding whether two drawn cubes could be the same cube. This test combines the two ideas with its own puzzles, so its scores can't be compared with the kit's.
For folding flat paper, try the Paper Folding Test; for turning shapes in your head, the Mental Rotation Test.