Pie

If n cuts are made in a pie, what is the largest number of pieces that may be obtained?

 

I draw some pictures and decided that the number is maximum if all the former cuts have been crossed (not at any point of intersections.

This is the pattern that I found.

 

number of cuts  n	1	2	3	4	5	6	7
number of peices   P	2	4	7	11	16	22	29

 

Now I looked to find the pattern,, with each cut the increaded number of peices  is 1 more than last time.

i mean 2+2=4, 4+3=7, 7+4=11

it will be a quadratic function. 

 

nunber of cuts  n	1	2	3	4	5	6	7
n(n+1)	2	6	12	20	30	42
n(n+1)+2 = n^2+n+2	4	8	14	22	32	44
(n^2+n+2) /2	2	4	7	11	16	22
number of peices   P	2	4	7	11	16	22	29

 

 

So the maximum number of peices if the cake is cut linearly n times is  (n^2+n+2)/2