A trick by Don Knuth eventually evolved into the so-called Kernel
method. It is used to solve a certain type of recursions. We report
about some applications. One is like this:
A deck of cards consisting of 
red and 
black cards is given. A
guess is made as to the colour of the top card, after which it is
revealed and discarded. To maximise the number of correct guesses one
chooses the colour corresponding to the majority of cards remaining in
the deck. We determine the expected number of correct guesses with
this strategy, as well as the probability of beating an opponent (a
child) who uses the naive strategy of random guessing.
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Please send comments and corrections to Thomas Klausner.