Before And Afterexpert series

More bean-counting. This is considerably more difficult than the “Jelly Beans” puzzle in the Beginner list. I won’t spoil your enjoyment by doing it for you – in any case, there are several ways to tackle it. One hint is that you may find it useful to define not only functions for the numbers of beans before and after, but more generally one giving the numbers of beans at each timestep (i.e. after each of the four transfers).

OK, same four kids, different jellybeans. At the start of this exciting adventure, they each have a different number and all the numbers are greater than 1 and less than 10. David gives some (one or more) of his beans to Alice, and Claire gives some but not all of hers to Boris. Then Boris gives some to Alice (lucky Alice!) and David gives some to Claire. All of the numbers of beans given in these transfers are different, and each is less than 7.

As a result of all that, they again each have a different number, and again all the numbers are greater than 1 and less than 10. No child has the same number of beans after as any child (themselves included) did before.

At the end, Alice has one more than David and Claire has one less than Boris.
Alice gets more from David than she does from Boris.

How many does each of them have, before and after?

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