We finally got round to going through an old storeroom in Quiz Master Shop Towers. It's the sort of place that you keep stuff for years and then throw it out a week before you need it!
On a dusty shelf we found an odd length of chain. It had straight links about a foot long, each link joined to the next with a small ring. The were nine of the straight links, and someone had joined the two ends together to make one loop. We could work out that this was done later as the ring was different from the others.
Of course, once we had found this oddity work on clearing the storeroom came to a halt!
We speculated as to the original purpose of the chain - perhaps a surveyor's chain - and amused ourselves making shapes from it. We discovered that we could only make three triangles from this chain, a surprisingly low number we thought. These are 4-4-1, 4-3-2 and 3-3-3 in terms of links.
We then took to discussing how many triangles we would have been able to make had the chain had more links.
And thus the puzzle is: how many links would need to be in the chain to make ten different triangles? Obviously we want to know the smallest number of links where this is possible.
It turns out that 19 links are needed. The triangles are 9-9-1, 9-8-2, 9-7-3, 9-6-4, 9-5-5, 8-8-3, 8-7-4, 8-6-5, 7-7-5 and 7-6-6.