(a) Suppose that there is a piece of paper with an m n grid drawn on...

 

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(a) Suppose that there is a piece of paper with an m n grid drawn on it (m, n are positive integers). Suppose that you want to cut the grid into 1 1 squares by cutting along the grid lines. Every cut can only cut one piece of paper at once (so you can't be more efficient by lining up multiple sheets of paper with a single cut). Show, using strong induction, that the number of cuts required is mn - 1. (b) Phrase and prove an appropriate version the proposition in part a for 3 dimensions. State what you expect the result should be in d dimensions. (a) Suppose that there is a piece of paper with an m n grid drawn on it (m, n are positive integers). Suppose that you want to cut the grid into 1 1 squares by cutting along the grid lines. Every cut can only cut one piece of paper at once (so you can't be more efficient by lining up multiple sheets of paper with a single cut). Show, using strong induction, that the number of cuts required is mn - 1. (b) Phrase and prove an appropriate version the proposition in part a for 3 dimensions. State what you expect the result should be in d dimensions.

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a Let Pk be the statement that in order to cut a k x n grid into 1 x 1 squares the number of cuts re... View the full answer