SP10105 ALPHSOUP - Alphabet Soup

- Peter is having lunch at home. Unfortunately for him, today’s meal is soup. As Peter’s mother is aware that he doesn’t like it very much, she has cooked a special soup using pasta pieces shaped like letters from the alphabet, numbers and other characters. She has a special knife with which she can prepare an unlimited supply of pasta pieces that may come in _S_ different forms. The soup always has _P_ pasta pieces in it, and is so thick that the pieces never move. Despite her efforts, Peter is still not happy with today’s menu and asks how many days in his life he will have to eat soup. His mother promises him that she will prepare a different soup every day, and that on no day will the dish contain the same shapes in all positions as any soup dish previously served. However, the number _P_ of pasta pieces, as well as the positions in which pieces float, will remain the same every day. Peter is not easily fooled (or so he thinks), and he cleverly realizes that this can still make him eat soup for ages. In an attempt to reduce the number of configurations, he tells his mother he will not accept any dish which can be obtained by rotating one of the configurations previously seen. > - - - - - -

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