How many pieces of cheese we can obtain from a single thick piece by making...

Arraryeldergox2

Arraryeldergox2

Answered

2022-06-25

How many pieces of cheese we can obtain from a single thick piece by making five straight slices? (we can't move the cheese when slicing) If we want to maximize the number of pieces which is denoted by P ( n ), is there any recurrence relation for P ( n ), where n is the number of slices?

Answer & Explanation

iceniessyoy

iceniessyoy

Expert

2022-06-26Added 27 answers

This is a special case of the problem of counting the number of regions R n is divided into by k hyperplanes in general position. The answer is
j = 0 n ( k j ) .
Zion Wheeler

Zion Wheeler

Expert

2022-06-27Added 11 answers

This is the lazy caterer's sequence. As others have mentioned, arbitrary dimensional analogues are called hyperplane arrangements.

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