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26 replies to this topic

#1 unreality

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Posted 03 March 2008 - 04:08 AM

1.
Consider a 5x3 rectangle- it is 5 unit squares wide and 3 unit squares tall, thus made up of 15 little squares. If you shade the outside squares, the border squares, 12 squares are shaded, with 3 in the middle left unshaded.

Can you make rectangle with its border squares shaded so that the number of shaded squares equals the number of squares in the center? If so, how many rectangles (including squares) like that can you make? What are the dimensions of those rectangles?

Spoiler for Hint



2.
A guy was having a paper written in English translated into French. He got the assistance of a French translator named Jacques. At the bottom of the paper was the following: (written in French of course)

"Much thanks to my friend Jacques for translating the above paper into French."

and then:

"More thanks to my friend Jacques for translating the above sentence into French."

and then:

"More thanks to my friend Jacques for translating the above sentence into French."


At first glance, this would have to continue forever, for proper thanks to be due. But it doesn't need too... it can (and does) end right there. Why?

Spoiler for Hint

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#2 bonanova

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Posted 03 March 2008 - 04:56 AM

Spoiler for Question #1 ...
Spoiler for Question #2 ...

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#3 storm

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Posted 03 March 2008 - 05:52 AM

Spoiler for For 1: Solutions


Spoiler for For 2

Edited by storm, 03 March 2008 - 05:53 AM.

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#4 Lausus

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Posted 03 March 2008 - 09:21 PM

Spoiler for Question #2 ...


But the riddle says he was having a paper written in English translated into French. That sounds like he wrote the whole thing, including those last three lines, and then submitted it to Jacques. He couldn't have known the translation before hand to have included it.

Edited by Lausus, 03 March 2008 - 09:22 PM.

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#5 bonanova

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Posted 03 March 2008 - 09:39 PM

But the riddle says he was having a paper written in English translated into French. That sounds like he wrote the whole thing, including those last three lines, and then submitted it to Jacques. He couldn't have known the translation before hand to have included it.

The OP is not clear about who wrote the original paper.
The action of the "guy" was to have Jacques translate the paper; for that, he wanted to credit Jacques.
Reasonably, then, the credits were written [in English] after the translation.
The credits then needed to be translated; and that required the additional credits.
Make sense?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 Lausus

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Posted 03 March 2008 - 09:43 PM

The OP is not clear about who wrote the original paper.
The action of the "guy" was to have Jacques translate the paper; for that, he wanted to credit Jacques.
Reasonably, then, the credits were written [in English] after the translation.
The credits then needed to be translated; and that required the additional credits.
Make sense?


I admit that makes the most sense. It's probably the answer. Though it seems a little unreasonable that the paper should be returned by the translator, a sentence added, and then given back. The OP implies the credits were written before the translator got hold of the paper.
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#7 unreality

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Posted 03 March 2008 - 10:30 PM

bonanova is correct :D

the "guy" wrote it in English, later getting the help of Jacques to translate it, and then leave a thank you message (and a thank you message for translating the thank you message, and then again, and so on... or not). Storm, the amount of paper doesn't matter- there's a logical solution as to why it's not an infinitely repeating line.

The answers and my methods:

Spoiler for Number One


Spoiler for Number Two

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#8 EventHorizon

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Posted 03 March 2008 - 10:36 PM

Spoiler for answer

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#9 unreality

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Posted 03 March 2008 - 10:42 PM

EventHorizon, 0x0 wouldnt be a rectangle ;D it would be a single point. Like how 1x0 rectangle is actually a line.

A 0x3x3 rectangular prism isnt actually a 3d rectangular prism as one of its dimensions is 0- it's a 2-dimensional object, as geometry goes. If a dimension is 0 then it's not counted as a dimension in geometry- it has to have some value to extend the axis in that direction. We don't say that a square has 5 dimensions if its 0x0x0x2x2, know what i mean?
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#10 statman

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Posted 03 March 2008 - 10:59 PM

1.
Consider a 5x3 rectangle- it is 5 unit squares wide and 3 unit squares tall, thus made up of 15 little squares. If you shade the outside squares, the border squares, 12 squares are shaded, with 3 in the middle left unshaded.

Can you make rectangle with its border squares shaded so that the number of shaded squares equals the number of squares in the center? If so, how many rectangles (including squares) like that can you make? What are the dimensions of those rectangles?

Spoiler for Hint



2.
A guy was having a paper written in English translated into French. He got the assistance of a French translator named Jacques. At the bottom of the paper was the following: (written in French of course)

"Much thanks to my friend Jacques for translating the above paper into French."

and then:

"More thanks to my friend Jacques for translating the above sentence into French."

and then:

"More thanks to my friend Jacques for translating the above sentence into French."


At first glance, this would have to continue forever, for proper thanks to be due. But it doesn't need too... it can (and does) end right there. Why?

Spoiler for Hint

Spoiler for Number 1

Spoiler for number 2

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