2018 IGO Elementary level P1

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High School Math Grades 9-12, Ages 13-18

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2018 IGO Elementary level P1

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bgn

#1 h Sep 20, 2018, 7:01 AM • 1 Y

Y by Adventure10

As shown below, there is a $40\times30$ paper with a filled $10\times5$ rectangle inside of it. We want to cut out the filled rectangle from the paper using four straight cuts. Each straight cut is a straight line that divides the paper into two pieces, and we keep the piece containing the filled rectangle. The goal is to minimize the total length of the straight cuts. How to achieve this goal, and what is that minimized length? Show the correct cuts and write the final answer. There is no need to prove the answer.

Proposed by Morteza Saghafian

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#3 h Sep 20, 2018, 10:00 AM • 2 Y

Y by Adventure10, Mango247

Is it 65??

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InternetPerson10

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InternetPerson10

#4 h Sep 20, 2018, 10:20 AM • 2 Y

Y by Adventure10, Mango247

Solution

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#5 h Sep 20, 2018, 10:23 AM • 2 Y

Y by Adventure10, Mango247

yes! But how can we prove this is shortest length??

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#6 h Sep 20, 2018, 10:25 AM • 2 Y

Y by Adventure10, Mango247

enthusiast101 wrote:

yes! But how can we prove this is shortest length??

Well, there are only $4!=24$ "optimal" ways to cut the paper, which is just a few. It suffices to check them all.

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InternetPerson10

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InternetPerson10

#8 h Sep 20, 2018, 10:26 AM • 2 Y

Y by Adventure10, Mango247

It might just be casework XD

Try cutting horizontally first (making a cut of length 40). whatever you do next, you can't get lower than 65.
Then, try cutting the left edge first. The next cut must be of length 30. Since we need to make two more cuts (at least 5), this won't work.
Then check all cases for cutting the right edge first - you'll find 65 to be the shortest.

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Shkev

#9 h Mar 17, 2019, 6:05 AM • 2 Y

Y by Adventure10, Mango247

There’s an answer key here from the official website: http://igo-official.ir/wp-content/uploads/2018/09/The_fifth_IGO_en.pdf#page6

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Eliti

#10 h Sep 12, 2019, 6:54 PM • 1 Y

Y by Adventure10

65 is answear thats easy

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