This is a classic puzzle that has been around for at least 250 years. It is very challenging, but it does give students a chance to get students up and moving. It depends on lateral thinking and topology (rubber geomettry or the mathematics of distortion). It can also make a good party game (for adults too).
For this puzzle you need
two people, some rope and some empty space to do the puzzle in. Each person
will need a piece of rope with a loop tied in both ends, so it can be worn
as handcuffs. The rope should be reasonably long, so that the person wearing
it can easily step over it if they want.
The Handcuff Puzzle Rules
The handcuffs cannot be removed.
Do not break, cut, saw through, bite through or in any other way damage the rope. Damaging each other is probably a bad idea too.
If you are doing this puzzle with a class, make certain you tell them they need to be able to show you their solution. Otherwise it won't be so enjoyable.
If you are showing this one to a class, some students will say that the puzzle is easy and they know how to do it. Don't worry, they don't. The first thing they will do is either step over the other person's rope or duck under it. This will not work.
People very rarely solve this one without assistance. Some hints that may help is to get them to stand within arms reach of each other, then tell them that they do not need to move their feet. Alternatively, explain to them that it is impossible to unlink two linked rings, but they are not two linked rings, there is a gap at each wrist.
If you are working with a single pair, you can lead them to the solution using a rubber band.
First have one student take off a handcuff, put the rubber band on their arm and get them to put the handcuff back on. Ask them to take the rubber band off their wrist without getting it caught on the rope. They will take it under the handcuff.
Next put the rubber band back on their arm but this time hold onto one point on the band. They will take it under their handcuff again, but this time they will have to stretch it over their hand and let it go back again.
Now use their partner's rope in the place of the rubber band.
If there was a gap in one handcuff or in your arm, the puzzle is easy to solve. You just need to move the other person's rope through the gap. To a topologist, this is no different to doing it when your wrist is in the loop. There is a gap between your rope and you; and you move the other persons rope through that gap. The only practical difference is that with the rope on your wrist there is a hand-shaped obstacle you need to move the rope around.
A single person version is to tie a knot in the rope, then put the handcuff on. They need to untie it, following the same rules.
Jill Britton Home Page
Copyright Jill Britton