Given the data in the book, I am aware that the most number of pieces you can produce with one cut is two, the most you can make with 2 cuts is 4 and the most you can make with 3 cuts is 7. In hopes of detecting a pattern in the number of pieces, I decide to make circles myself and draw in cuts. I started out with drawing two circles, and making one with four cuts and having one with five cuts.
Shown above are several possibilities for circles with four cuts and five cuts. I took me several circles with four cuts to finally realize that the maximum pieces you can have when you make four cuts in a pie, is 11 pieces. I did the same with 5 cuts, and it took me several tries to finally come to the conclusion that the max. number of pieces you can make with five cuts is 16. I finish the In/Out Table given in the book.
In (# of cuts) Out (max. # of pieces)
3. I notice a pattern in the number of pie pieces. The difference between 4 and 2 is 3, the difference between 7 and 4 is 4, the difference between 11 and 7 is 5. [continues]
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