Maximum number of slices can you obtain by cutting a cake with only 4 cuts?


A maximum number of 11 slices is attainable with 4 straight cuts.Assuming that after each slice cut we can not put all slice on top of each other.

A maximum number of 16 slices is attainable with 4 straight cuts.Assuming that after each slice cut we can put all slice on top of each other.

solution 1: (Assuming that after each slice cut we can not put all slice on top of each other.)
If you cut cake in traditional way like pizza.(Cutting through the center would give you 8 slices )

However, even more slices are possible if the cuts do not all intersect.
look at  lazy caterer’s sequence
The lazy caterer’s sequence describes the maximum number of pieces of a circle that can be made with a given number of straight cuts. The maximum number of pieces, p, that can be created with n cuts is given by the formula:
p = 1/2(n^2 + n + 2)
Therefore, for 4 cuts of the cake:
p(4) = 1/2(4^2 + 4 + 2) = 11
cut will look like:
solution 2: (Assuming that after each slice cut we can put all slice on top of each other.)

2^4= 16

step 1: cut the cake from middle in two equal pieces. this is the first cut and we get two pieces.

step 2: put one piece on the other piece vertically and cut them from top to bottom. this is the 2nd cut and we have 4 piece.

step 3: again put the 4 pieces on each other vertically and cut from top to bottom. this is 3rd cut and we have 8 piece.

step 4: again put all the 8 pieces on each other vertically and cut from top to bottom. this is the 4th cut and we have 16 equal piece.

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