Pow 13 Cutting the Pie

POW 13: Cutting the Pie

Problem statement: To find the largest number of pieces that can be produced from a given number of cuts.

1 2

2 4

3 7

4 11

5 16

6 22

7 29

8 37

9 46

10 56

Process: In this problem I drew circles to try to find out the answer. Those can be seen stapled behind this. That didn't help me with finding the answer. So I tried looking for patterns that were in the data table. I then found out that the difference between 4 and 2 is 2, the difference between 7 and 4 is 3, and the difference between 16 and 11 is 5. I didn't really know what I was doing when I did that so then I had tried to come up with a formula. It was really hard to find this equation. I realized that the number of cuts needed to be squared, and then added to itself. I had a hard time coming up with dividing by 2. I did a lot of adding and finally did divide by 2. Then it was one less so I added 1.

Solution:

In this table I noticed that as the number of cuts increased so did the number of pieces. I also noticed that the difference between 4 and 2 is 2, the difference between 7 and 4 is 3, and the difference between 16 and 11 is 5.

The largest possible number after 10 cuts is 56. I got this by using the formula

(X²+X)/2+1=number of pieces

Extension: If you have 50 cuts what's the largest amount of pieces.

50 ²+50=2550

2550/2=1275

1275+1=1276

If you had 50 cuts you would have 1276 pieces.

Self assessment: In this POW that if u looks for a pattern in the data it doesn't always help you solve the problem. Coming up with the rule was really tricky and took a while to do it, but once I got it the rest was pretty easy.