Problem 45394. Count the number of folds needed to pack a large sheet

Created by Karl Ezra Pilario

Solve Later

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In a certain paper factory, large sheets of paper are being made every day. Before sending the sheets for shipment, they have to be packed in a small case of length 1 foot and width 1 foot. This is done automatically by a robot, which is programmed to fold a large sheet of paper as many times as needed to fit it into the case. The following is the robot's algorithm:<ol><li>Lay down a large sheet of paper of size X-by-Y feet.</li><li>Fold the sheet in half so that the larger length between X and Y is halved and the other length remains the same.</li><li>Repeat step 2 until both lengths X and Y are less than 1 foot.</li></ol>For this problem, you can assume that the thickness of the paper is irrelevant. You are then given the following task by the company manager: Write a function that determines the number of folds needed to pack a certain sheet of paper, given its initial dimensions X and Y. You are ensured that X and Y are integers given in feet, and that 1 &lt;= X &lt;= 4000 and 1 &lt;= Y &lt;= 4000.As an example, let the initial dimensions be (X,Y) = (4,5). The algorithm will produce the following sequence of paper sizes: (4,5) -&gt; (4,2.5) -&gt; (2,2.5) -&gt; (2,1.25) -&gt; (1,1.25) -&gt; (1,0.625) -&gt; (0.5,0.625). We stop because both sizes are now less than 1. This takes a total of 6 folds.

In a certain paper factory, large sheets of paper are being made every day. Before sending the sheets for shipment, they have to be packed in a small case of length 1 foot and width 1 foot. This is done automatically by a robot, which is programmed to fold a large sheet of paper as many times as needed to fit it into the case. The following is the robot's algorithm:

# Lay down a large sheet of paper of size X-by-Y feet.
# _Fold_ the sheet in half so that the _larger_ length between X and Y is halved and the other length remains the same.
# Repeat step 2 until _both_ lengths X and Y are _less_ than 1 foot.

For this problem, you can assume that the thickness of the paper is irrelevant. You are then given the following task by the company manager: Write a function that determines the number of folds needed to pack a certain sheet of paper, given its initial dimensions X and Y. You are ensured that X and Y are integers given in feet, and that 1 <= X <= 4000 and 1 <= Y <= 4000.

As an example, let the initial dimensions be (X,Y) = (4,5). The algorithm will produce the following sequence of paper sizes: (4,5) -> (4,2.5) -> (2,2.5) -> (2,1.25) -> (1,1.25) -> (1,0.625) -> (0.5,0.625). We stop because _both_ sizes are now less than 1. This takes a total of 6 folds.

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165 Solutions
56 Solvers

Last Solution submitted on Jun 02, 2021

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2 Comments

Roberto Mennella on 28 May 2021 at 10:32

Even if on the MATLAB software I can prove that my code works, here, I get the error that the server runs out of time. Can someone please help me with this?

Karl Ezra Pilario on 30 May 2021 at 6:38

It happens sometimes. You can just try later.

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