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A square piece of paper is cut by n different straight lines, each pas

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A square piece of paper is cut by n different straight lines, each pas  [#permalink]

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New post 19 Sep 2017, 10:25
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  95% (hard)

Question Stats:

23% (01:59) correct 77% (02:34) wrong based on 65 sessions

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A square piece of paper is cut by n different straight lines, each passing through two parallel sides of the square. If no cut passes through any of the square's four vertices, what is the value of n?

(1) The sum of the perimeters of the smaller shapes into which the square is cut is exactly n times the perimeter of the original square.
 
(2) The n cuts divide the original square into two pentagons, three quadrilaterals, and two triangles.

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A square piece of paper is cut by n different straight lines, each pas  [#permalink]

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New post 05 Nov 2017, 10:07
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1. Only possibility is 2 cuts and perimeter is double of square.
If we add more cuts, we would have to get 3X, 4X, 5X of perimeter.. which is not possible.
So, n=2

2. Here also, only possible solution is n=3

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A square piece of paper is cut by n different straight lines, each pas &nbs [#permalink] 05 Nov 2017, 10:07
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