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

 Feb 12, 2018

Best Answer 

 #1
avatar+107446 
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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

 Feb 12, 2018
 #1
avatar+107446 
+2
Best Answer

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

Melody Feb 12, 2018

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