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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201 Solutions
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Last Solution submitted on Jan 01, 2022

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2 Comments

Roberto Mennella on 28 May 2021

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

It happens sometimes. You can just try later.

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