How many pieces of a regular round cake can you get with four straight cuts?

Question

For example with 3 cuts, we can get a maximum of 8 pieces. 
(Two cuts to get quarters and one cut horizontally across to get 8 pieces.)

So, what is the maximum number of pieces with 4 cuts.
Note that the pieces NEED NOT be the same size.

For the mathemtically savvy, you can provide a general solution.

Also, note that the cake pieces should not be moved during the cuts. That means, it is an in-place cut, the cake pieces remain in their original positions.

Demiurge42 · Accepted Answer

For the 4th cut, you can only cut through 6 of the pieces at most.  This gives you 14 pieces (8+6).

I guess I'm not math savvy as I a am not able to picture in my head how many 5 cuts can give you let alone how many in general.

With just vertical cuts you can have:
0 cuts = 1 piece
1 cut = 2 pieces
2 cuts = 4 pieces
3 cuts = 7 pieces (because you can only cut 3 of the previous pieces)
4 cuts = I think you can only cut though 4 of the previous pieces but I'm not sure.  This would give you 11 pieces. 

Then a horizontal cut doubles the pieces.

It looks as if the number of pieces you can cut through with the nth vertical cut is n.  So the number of pieces after the nth cut will be n more than the previous cut.  then with one more horizontal cut you can double the number of pieces.

Your Answer · Answer

four straight cuts in a round cake will give maximum 4*3 -- 1 = 11 pieces ANSWER

fizixx · Answer

If you obtain 8 pieces from 3 cuts, if you now cut the cake as a cross-section you double the number of pieces and end up with 16.

David · Answer

I guess it would be 12. Two cuts across, one cut vertically, and the last one through the cake.

Trending News

How many pieces of a regular round cake can you get with four straight cuts?

4 Answers