Find the length of the string

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HansV
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Find the length of the string

Post by HansV »

In today's The Guardian: Can you solve it? Are you in the smartest 10 per cent?
A string is wound symmetrically around a circular rod. The string goes exactly four times around the rod. The circumference of the rod is 4cm and its length is 12cm. Find the length of the string.
String.jpg
Note: only basic mathematics is needed.
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Hans

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Rudi
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Re: Find the length of the string

Post by Rudi »

Tip: If you go to the loo and unwind the inner cylinder of a standard toilet paper roll, and add 4 cm to its length, you'll almost be there.
(Now when the lounge becomes quiet, we'll all know where the members are!!) :grin:
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Rudi

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HansV
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Re: Find the length of the string

Post by HansV »

And now for the real answer...
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Hans

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StuartR
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Re: Find the length of the string

Post by StuartR »

Spoiler
If you cut the roll lengthwise then you will see the thread making lines across a rectangle. There are 4 lines, each of which is the hypotenuse of a 4x3x5 right angle triangle, so the total length is 5cm * 4 = 20cm
Roll.png
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HansV
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Re: Find the length of the string

Post by HansV »

That was my solution too. :thumbup:
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Hans

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StuartR
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Re: Find the length of the string

Post by StuartR »

I added a diagram to make it more clear
StuartR


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Rudi
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Re: Find the length of the string

Post by Rudi »

You guys and your math(s)!! Way to clever for me! :newbrain:
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PaulB
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Re: Find the length of the string

Post by PaulB »

Very clever!
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Rudi
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Re: Find the length of the string

Post by Rudi »

Question:
Spoiler
Out of interest, if you could not cut the roll to make it flat, would there be a clever way to work it out using pi or circumference or something like that, even though it might be a bit more complex than the request for a basic solution?

Some interesting formulas here:
- Lenth of line around an object
- Calculating Total Length of Wraps Around A Cylinder
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Rudi

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HansV
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Re: Find the length of the string

Post by HansV »

Spoiler
I don't think a more complicated calculation would help.

You don't even have to cut the cylinder open. In your imagination, apply some ink to the string, then roll the cylinder over a sheet of paper. You'll basically get Stuart's diagram. After four complete revolutions, you'll have a straight line representing the entire string.
S1681.png
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Hans

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AlanMiller
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Re: Find the length of the string

Post by AlanMiller »

Spoiler
As soon as I saw the 4 (circumference) and the 12cm/4 turns = 3, I knew a 3-4-5 triangle would appear somewhere. Sure enough it did.:grin:
Alan