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Lesson 3 of 11

Six squares, and most plans do not fold

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Six squares in a row. A cube has six faces. Does the row fold into a cube?

Six squares in a row.
Step 1 of 4
  1. Six squares in a row.
  2. Roll a cube along it.
  3. Squares 1 and 5 land on the same face.
  4. 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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