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        riddles >> hard >> Formation of the bigger square.
        
(Message started by: Wonderer on Dec 20^th, 2005, 6:43pm)

Title: Formation of the bigger square.
Post by Wonderer on Dec 20^th, 2005, 6:43pm

You have 3 identical paper squares, a pencil, a pair of scissors and a ruler (with no markings, so you can only use it to draw straight lines). You must cut these 3 squares into 9 pieces and use them to form a bigger square. How do you do it? (please attach diagrams to illustrate)

Note:
1 the ruler is only used for drawing straight lines
2 you are not allowed to fold the paper
3 since you only have 1 ruler, you can’t draw parallel lines

Title: Re: Formation of the bigger square.
Post by Grimbal on Dec 21^st, 2005, 2:16am

Technically, a paper square with a ruler could be used to draw parallels. Unless it is very thin paper.

Title: Re: Formation of the bigger square.
Post by rmsgrey on Dec 21^st, 2005, 11:43am

What about folding?

Title: Re: Formation of the bigger square.
Post by SMQ on Dec 21^st, 2005, 11:49am

on 12/21/05 at 11:43:26, rmsgrey wrote:

What about folding?

Er, I believe that's covered by note 2, unless you want to try to fold the ruler, scissors, or pencil?

--SMQ

Title: Re: Formation of the bigger square.
Post by rmsgrey on Dec 21^st, 2005, 11:54am

on 12/21/05 at 11:49:28, SMQ wrote:

Er, I believe that's covered by note 2, unless you want to try to fold the ruler, scissors, or pencil?

--SMQ

Must learn to read...

Title: Re: Formation of the bigger square.
Post by Sjoerd Job Postmus on Dec 21^st, 2005, 11:41pm

surface of 3 identical squares = 3 a^2
surface of larger square = b^2

b^2 = 3 a^2
b = a*sqrt(3)

Assuming a = 1, where can we find sqrt(3)? The diagonal would be sqrt(2). But, we know that sqrt(3) is most often found as sqrt(2^2 - 1^2)
Yet, it's difficult to find sqrt(3)... Because the length of a line in the square x can be expressed as: width <= x <= width*sqrt(2)...

So, we must find it in a set of two squares...

I assume I can draw on the ruler... like, make markings at lengts I want to.... The fact that it's unmarked doesn't mean I can't mark it...

Sure, I'm only allowed to draw straight lines with it, according to you, but I'd like to lie the ruler next to two squares, and mark the ruler... (with a straight line :P)

Title: Re: Formation of the bigger square.
Post by Barukh on Dec 22^nd, 2005, 3:57am

Is the following construction allowed? I guess that's similar to what Sjoerd had in mind. The length of the thick line is [sqrt]3.

If that's allowed, the problem can be solved with just 7 pieces.

Title: Re: Formation of the bigger square.
Post by Wonderer on Dec 22^nd, 2005, 9:52pm

on 12/22/05 at 03:57:01, Barukh wrote:

Is the following construction allowed? I guess that's similar to what Sjoerd had in mind. The length of the thick line is [sqrt]3.

If that's allowed, the problem can be solved with just 7 pieces.

Yes, this is allowed! in fact, you can do it with 6 pieces.

Title: Re: Formation of the bigger square.
Post by Barukh on Dec 23^rd, 2005, 12:18am

on 12/22/05 at 21:52:57, Wonderer wrote:

Yes, this is allowed! in fact, you can do it with 6 pieces.

Yes, I know.

But I thought the attached 7 pieces dissection is more suited for the tools and restrictions of the problem. The dashed lines indicate the cuts.