Miss Priya is the teacher of a large class of girls at one of our more enterprising schools.She is responsible for several subjects, including what is vaguely called "handwork", but herprincipal interest is in mathematics."I tried an interesting experiment this week," she told me. "I had available a large number of beads. They were of three colors: red, yellow, and green"."I showed my girls how to make seven-bead bracelets-the beads are just strung on threads atregular intervals-and then I suggested that each girl should make a bracelet for herself. Myonly condition was that she should use three beads of any one color; two of a second color;two of a third"."And what was the experiment exactly?" I asked. "Why," said Miss Priya, "I wanted to seehow many different bracelets were produced by these haphazard instructions. There werethirty-two, which is about what might have been expected. It would have been possible-butonly just possible-for every girl to construct a bracelet different in appearance from all theothers."How many girls are there in the class?

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