wu :: forums
wu :: forums - 21 squares (solution)

Welcome, Guest. Please Login or Register.
Jun 24th, 2018, 4:11am

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   hard
(Moderators: Grimbal, SMQ, ThudnBlunder, towr, william wu, Icarus, Eigenray)
   21 squares (solution)
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: 21 squares (solution)  (Read 1481 times)
tim
Junior Member
**





   


Posts: 81
21 squares (solution)  
« on: Jul 28th, 2002, 12:40am »
Quote Quote Modify Modify

I was attracted to this one because it claimed "calculator/computer power".  Them's fightin' words Smiley
 
It looked like one that I could do with pencil and paper at worst. And it turned out to be so.
 
My first approach was to look at the smallest squares, and guess that they had small integer values. First I tried n=1, and guessed s=2n and i=3n visually. Each internal line gave equations for the sum of sizes of squares on either side. Solving a few of these led to o=3.5, so I bumped n up to 2.
 
With a combination of eyeballing relative sizes (i.e. guessing) and a little equation-solving, I managed to find a set of sizes that satisfied all the equations. As it turned out, the first four relative sizes I guesses were right.
 
If that hadn't worked, I expect I would have written down all the linear equations and solved them by brute force Smiley
 
Enough rambling. The solution:
a=50, b=35, c=27, d=8, e=19, f=15, g=17, h=11, i=6, j=24, k=29, l=25, m=9, n=2, o=7, p=18, q=16, r=42, s=4, t=37, u=33.
IP Logged
Nicodemus
Guest

Email

Re: 21 squares (solution)  
« Reply #1 on: Jul 28th, 2002, 2:44pm »
Quote Quote Modify Modify Remove Remove

That works, Tim. I think that's how it's supposed to be done. But this also occurred to me:
 
It's designated "CPU" so we can use a computer to solve it. The problem is presented as a digital image... composed of discrete pixels. Load it into photoshop and measure regions in pixels. Smiley
IP Logged
tim
Junior Member
**





   


Posts: 81
Re: 21 squares (solution)  
« Reply #2 on: Jul 28th, 2002, 3:35pm »
Quote Quote Modify Modify

Unfortunately that doesn't work: the image is 216x216 pixels, while the only integer solutions are multiples of 112 pixels. :/
 
If you actually carried out this procedure, you would be tripped up by the blurry edges of the squares.  You would have to decide for each square whether it was really x pixels or x+1 pixels in size, and would find that neither choice worked in the big picture.
 
That might lead you to erroneously conclude that the problem had no solution.
 
Nice try, though  Wink
IP Logged
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright 2000-2004 Yet another Bulletin Board