Six unit squares can be joined
along their edges to form 35 different
hexominos, the simplest being a one
by six rectangle.
How many of these
hexominos can be folded along edges
joining the squares to form a unit
cube?
A rotation or reflection is not
considered to be a different hexomino.
***Adapted from a problem appearing in The BENT, Brain Ticklers,Spring Collection 2008.
This is way too easy to research for a solution. Just looking for the an illustration of the set of hexominoes the
wikipedia article for Hexomino shows you the answer to this question later in the article.
They also suggest an efficient method of weeding out non-solutions: look for the subshape of the square tetromino, or the I, V or U pentominoes. Trying to fold any of these smaller polyominoes over a cube will result in overlap.
This is very effiective since 21 of the 35 hexominoes have at least one of these subfigures and can be ruled out.
Research
