A useful group and an uninteresting operation

Extract

I am continually surprised by the mathematical structure which surfaces in unexpected situations, and even more so when arranging a tenth birthday party for my elder son. The invasion of the home by some eight rather energetic boys on a cold February afternoon was viewed with some trepidation. The instinct of self preservation was uppermost in the search for activities which would allow the afternoon to pass with the minimum of discomfort and the maximum enjoyment. A family friend is very good at organising team games at parties, but with a space problem (our house does not have a large living room as so many modern houses have these days) it was important to split the children up for their activities, but yet devise a programme which was coherent.