From: baustad@idt.unit.no (Jostein Baustad)
Newsgroups: rec.puzzles
Subject: Re: Brick Problem (crude ASCII)
Keywords: brick, graphical, puzzle
Date: 7 Apr 92 16:48:04 GMT
Reply-To: baustad@idt.unit.no (Jostein Baustad)
Organization: Norwegian Institue of Technology

In article <orange.702580580@cunews>, orange@alfred.carleton.ca (Paul Vallee) writes:
|> 
|> Here's one I've been toying around with while bored in class for
|> awhile, but I've ony managed to solve one of them.  An uncle described
|> these to me as being solvable, so don't give up... (that is, if you
|> believe my uncle. :)
|> I myself have only been able to solve one of them.  I won't tell you which.
|> 
|> Ok, here, in crude ascii, is a picture of a brick wall, with three
|> bricks on top, two on the middle row, and three again on the bottom
|> row.
|> The object is to draw a curvilinear line through every wall of every
|> brick, without going through any given wall more than *once*.
|> Note:  Bricks in the middle row have *six* walls, ok?  I can't think
|> of a better way to describe this.  Center bricks on the top and bottom
|> rows have *five* walls.
|> 
|>   |----|-----|----|
|>   |    |     |    |
|>   |----|--|--|----|
|>   |       |       |
|>   |----|--|--|----|
|>   |    |     |    |
|>   |----|-----|----|
|> 
|> To simplify your description of a solution, here is a lettering scheme
|> we may convene to use:
|> 
|>      a    b     c
|>   |----|-----|----|
|> d |  e |  f  |  g | h
|>   |----|--|--|----|
|> i |   j   |    k  | l
|>   |----|--|--|----|
|> m |  n |  o  |  p | q
|>   |----|-----|----|
|>      r    s     t
|> 
|> i.e. To describe a solution beginning at o, and going to the right,
|> o, p, q, l, k, g, h, etc...  get the picture?
|> 
|>

Its obvious that you must start in one brick with five walls, i.e. the brick
with the letter o in it, and end in the other, i.e. brick f:

Here is one solution:
o,s,r,n,m,i,j,n,o,j,e,d,a,e,f,b,c,g,f,k,g,h,l,k,p,q,t,o,k,j,f (puh!)
 
|> Same problem, different brick layout...
|> 
|> 
|>   |-------|-------|
|>   |       |       |
|>   |----|--|--|----|
|>   |    |     |    |
|>   |----|-----|----|
|>   |       |       |
|>   |-------|-------|
|> 
|>       a       b
|>   |-------|-------|
|> c |   d   |   e   | f
|>   |----|--|--|----|
|> g |  h |  i  |  j | k
|>   |----|-----|----|
|> l |   m   |   n   | o
|>   |-------|-------|
|>       p       q
|> 
|> 
|> Good luck...
|> 
|> 

Unless I am missing something (I assume the line must be continous), I don't
believe your uncle! The bricks with the letter d, e, m and n all have 5 walls
each (an odd number). If you start in one 5-wall brick and end in another, this still leaves two 5-wall bricks where the line must pass through. And it is
clear that this is impossible - the number of walls has to be an even number.

|> -- 
|> 
|> 
|> orange@ccs.carleton.ca ------- Paul Vallee ---- 542429@acadvm1.uottawa.ca
|> ------------Home: (613)569-1068 --------- Work: (613)995-6921------------
|> "Like chewing on glass, and burning my fingers,
|>         I'm not the one who's run out of lies..." - Stigmata, by Ministry

Jostein

-- 
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* Jostein Baustad                    * E-mail : baustad@idt.unit.no           *
* Norwegian Institute of Technology  *          baustad@solan.unit.no         *
* Division of CS and Telematics      * "Reality is just a convenient          *
* Information and Knowledge Systems  *  measure for complexity."              *
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*             Queen's Park Rangers F.C. - SuperHoops !                        *
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