This puzzle comes from a wonderful Russian site, where its solution is presented as a sequence of animations. (A later remark: through the efforts of Colm Mulcahy who approached David Singmaster an earlier reference has been found: Martin Gardner describes the puzzle at the end of Chapter 5 of his New Mathematical Diversions - a book from 1995.)
Is it possible to wrap the cube with a 3×3 piece of paper below it? Handling of the paper is subject to two conditions:
- The paper may be only cut or folded along the crease lines.
- The cutting should not cause pieces to separate.
There are three "cut-and-fold" operations:
This leads to a 3-step stair-like design. Place the cube on one of the middle squares:
Now, fold the paper: