Henry Ernest Dudeney/Modern Puzzles/214 - Folding Postage Stamps

by : $214$

 * Folding Postage Stamps
 * Take a $4 \times 2$ sheet of $8$ postage stamps, labelled $1$ to $8$, as shown in the diagram.
 * It is an interesting exercise to count how many ways they may be folded up so they will all lie under the one stamp, as shown.


 * Dudeney-Modern-Puzzles-214.png


 * There are in fact $40$ ways to do this so that No. $1$ is always on the top.
 * Numbers $5$, $2$, $7$ and $4$ will always be face down.
 * You can always arrange for any stamp except No. $6$ to lie next to $1$,
 * although there are only two ways each in which $7$ and $8$ can be made to lie in that position.


 * ''They can be folded in the order $1$, $5$, $6$, $4$, $8$, $7$, $3$, $2$ and also $1$, $3$, $7$, $5$, $6$, $8$, $4$, $2$, with $1$ at the top face upwards,
 * but it is a puzzle to work out how.


 * Can you fold them like that without tearing any of the perforations?