Six squares, and most plans do not fold
Six squares in a row. A cube has six faces. Does the row fold into a cube?
- Six squares in a row.
- Roll a cube along it.
- Squares 1 and 5 land on the same face.
- Squares 2 and 6 land on another; two faces stay bare.
No, the row does not fold into a cube. Two faces get two squares each, and two faces get none.
Rule: Roll a cube along the plan, one square at a time. Six squares on six different faces close the cube.
Two squares on one face is an overlap. A face no square reaches is a gap.
Only three faces meet at a cube corner. So four squares around one point cannot fold into a cube.
There are 35 ways to join six squares edge to edge. Only 11 of them fold into a cube.
Watch out!
A cross is a row of four squares. It also has one square above the row and one below. Not every plan that folds looks like a cross. A staircase of three steps folds into a cube too.
Tap squares to change the plan. Make six that fold into a cube.
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