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?

Question

How many pieces of cheese we can obtain from a single thick piece by making five straight slices? (we can&#039;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?

iceniessyoy · Accepted Answer

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 · Accepted Answer

This is the lazy caterer&#039;s sequence. As others have mentioned, arbitrary dimensional analogues are called hyperplane arrangements.