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. Colm Mulcahy later reported that the article was included into Gardner's 1966 Third book of Mathematical Diversions from Scientific American and later added that the original column appeared in 1960.))
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: