wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> easy >> shape into three 
        
(Message started by: Ez Hassan on Jul 19^th, 2005, 5:43am)

Title: shape into three
Post by Ez Hassan on Jul 19^th, 2005, 5:43am

Hello everybody,
I have been thinking about this for the longest time. But i seem not to be able to get the goal is to cut the shape onto three congurent shapes ( along the squares).
four is so easy but three seems impossible Help please

Title: Re: shape into three
Post by Ez Hassan on Jul 19^th, 2005, 5:48am

sorry here is the puzzle
http://user.cs.tu-berlin.de/~yoki/riddle/sit.html

Title: Re: shape into three
Post by towr on Jul 19^th, 2005, 10:29am

note that it doesn't say 'along the lines' there..

Title: Re: shape into three
Post by Ez Hassan on Jul 19^th, 2005, 10:36am

well could it be done along the lines?

Title: Re: shape into three
Post by towr on Jul 19^th, 2005, 2:22pm

I'm pretty sure it isn't possible. But I don't see a clever way to prove it (just trying all possibilities).

Title: Re: shape into three
Post by JocK on Jul 19^th, 2005, 3:37pm

when not following the lines, dividing it into three congruent pieces is trivial...

Title: Re: shape into three
Post by SWF on Jul 19^th, 2005, 7:54pm

It is impossible to do it by cutting only along the lines. Due to 4 of the small squares only touching one other square, 4 dominoes (pairs of squares) are immediately identified such that each of them is entirely within one piece. With 3 pieces, two of those dominoes must both be in one of the pieces. Just try the 3 ways of pairing up two in one piece, and it is pretty easy to see that this is impossible.

Title: Re: shape into three
Post by EzisEz on Jul 20^th, 2005, 6:37am

well, how about cutting it along the squares in not ( nessecarly,contiuous shapes( only joined by the edge of the little squares???

Title: Re: shape into three
Post by raprap on Jul 23^rd, 2005, 6:09am

;DThinking outta box here.

Cut into two shapes along the horizontal. Rearrange putting the tab and indents together making a 4 by 6 rectangle.

Then divide this rectangle with two vertical cuts into three identical 2 by 4 rectangles.

Rap