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'Link Puzzle' printed from http://nrich.maths.org/
I was at a meeting with a colleague from the local Science
Learning Centre and she had this metal "puzzle" on her desk.
I know I should have been focussed on what was being discussed
at the meeting but I was distracted by the way the puzzle had been
made and its mathematical properties. I hope this image helps you
to see that the puzzle is made from sections of circular rings all
joined so that each section can be rotated against the next.


I first wondered how much each arcshaped segment contributed to a
full turn and so I tried to lay all the rings out flat...
and ended up with this:
This certainly confirmed for me what angular contribution each
section of the puzzle makes, and that got me thinking...
Firstly, about the number of sections that have to curve "in" and
the number that have to curve "out". Look at the image and see if
the answer in this case makes sense.
Secondly, I wondered whether there were other ways I could
"flatten" the puzzle. It occurred to me that in fact this picture
is a cheat. Can you explain why? You might find the interactivity
below helpful or the arcs I created on paper
here .
Can you find any rules about the number of curves you need to make
a closed arc? Are there any other properties of the resulting
closed curves you can identify?
The puzzle was supplied by Frank
Ellis of GlaxoSmithKline.