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

Modern Puzzles by Henry Ernest Dudeney: $214$

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.

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?

Solution

To get the order $1$, $5$, $6$, $4$, $8$, $7$, $3$, $2$

Fold $7$ over $6$.

Lay $4$ flat on $8$.

Tuck them both in betwen $7$ and $6$ so these four are in order $7 \, 8 \, 4 \, 6$.

Bring $5$ and $1$ under $6$, and it is done.

To get the order $1$, $3$, $7$, $5$, $6$, $8$, $4$, $2$

Fold so that $5 \, 6 \, 7 \, 8$ only are visible with faces uppermost.

Fold $5$ on $6$.

Between $1$ and $5$ you have to tuck $7$ and $8$, so $7$ lies on top of $5$ and $8$ ebnds under $6$.

The stamps will now be in the required order.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $214$. -- Folding Postage Stamps
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $367$. Folding Postage Stamps