Once again, even BuBe couldn't do this w/o a computer program. This is WAY beyond CAB=(AB)^2.
I hope and trust I have not spoiling anybody's fun trying to do this. You might have got to the stage where you realized it had to be four rectangles around the edge and one in the middle (visualizing what the necessary Geeometree had to be was key) and you may also have started writing down equations the sides had to obey (or maybe not) but keeping ten nested loops in your head ... that might have proved challenging.
Please visit http://primepuzzle.com/tc/tile.html for the details.
19 comments:
BuBe's mind on other things right now, but love checking in to see what the brains of the operation are doing these days!
Can you write your solution so that the dimensions of each rectangle is given (e.g. 10 x 2, 3 x 5, etc). That is how my answers are written. Tanx.
I just realized this problem is sort of like the "square dance" problem we talked about some time back. Here 10 "edges" are paired up and, instead of the sum of the numbers for each pair adding up to a perfect square, the products of the numbers in each pair have to sum to a perfect square.
In case you cared.
Obviously, I really enjoyed this one.
TcT
Once again, TcT succeeds! I never really thought about a perfect square was called that 'cause it makes a square. Purdy cul. I have a very special star for you, and will post it later. I would like to see your program you made for this also.
Id iz indereztin ow da numbah ov cuisanaire (sp?) rods in each rectangle corresponds tah wun ov da sides ov each wun.
There's a link to the tiny-c program at the bottom of http://primepuzzle.com/tc/tile.html
The stah scope is very very beautiful. Thanks so much DeeDee. I look forward to learning how you did this. And I will look into your idea of generating them w/ a program.
Max, I know you're busy, what w/ moving, painting, working, running two blogs, thinking, running, whatevering ... but would you be at all interested in taking a stab at trying to understand, *in a very general sense*, how my tile.tc program works and then writing, *in 100 words or less*, something in English that Joe Anybody could actually understand which explains the main ideas?
Dais iz a vewy cul tiling fourmat quezhun u hav answered in a reelee cul way. DeeDee's stah foah u iz definitlee cul too. (Luks lyke a Boo Giant tah mee) Ize hav lookeed at yur prograym and Ize tink Ize might be able tah za sumding in 100 wurds or lezz dat anybody wiyill be able tah udderstaynd. Whin Ize getz a moment, Ize wiyill put sumding togetha foah awl ov u. By da way, dais must hav bin a reyal challenge tah create. Da ding dat iz pritty cul aboot id iz dat id zur MUST hav bin challenging tah keep trak ov zo many "if dais kuller and length blawk goz heah, denn(s)." Nyce wuk! Nyce Stah!
I can do it on graph paper, it took a few sheets, but I did it.
Wow. I just realized I have to get a lot done in the next few days (like move out by 2/28). I will have to take a break awn dais. See you all on the uddah side ov my moove. Have fun. Buy nuhow.
One of these days I'm going to have to try the "BuBe Method," which goes something like this: think about the actual problem and try things till you get it. This is in contrast to "The TcT Method" which goes something like this: completely avoid the specific problem, abstract it completely and let a computer carry out millions and millions of instructions till it tells you what actually thinking it out would tell you. I also scribbled a variety of fairly unreadable jibberish on several sheets of paper before I coded it up. My guess is it took us both about the same amount of time and paper. Different Strokes for Different Folks.
Ize gezz theah iz always mowa dan wun way tah....um, maybee datz nutt suech a gud zayin awn dais blog! Graph papah, brilliant BuBe, Ize nevah thod ov id. And ov course figuring owd a compooter prograym iz brilliant alzo.
Ize am glad u 2 enjoyed da poozle. Ize tink Max juz figured owd dat id iz da shortest munth ov da yeer! Maybee he cayne tri id owd aftah he gets settled.
This really has nothing to do with the Tile a square poozle but I just wanted to say DeeDee's (Max-inspired) "rectangles" image in her "Geeometree" poast has, along w/ three other recent Toby images, been included in the images that randomly appear when you go to the online translator. These images are no longer "background" images but appear at the bottom of the page. The page now includes a link to the "offline" translator (the one you use under DOS (or Linux)).
I need to add her new wurd Geeometree and my new wurd mollykewelar, which, in case you missed it was used on Math4Chip.
"And then ... the miracle of mollykewelar rearrangement awaits you ... what other "construction" lines could you pull out of your brain?"
DeeDee's Toby images are so creative!
I have to say that I would not win any contests in speedy response times. I struggled with that one, but it was fun. And TcT, if we broke down all the different steps I went through to solve this (in Montessori step detail) it would probably be same number of instructions you gave your computer. Personally, I think I just got lucky whereas you actually have some skills involved. LOL
That is a humble way to put it. It may be true you got lucky but I would not underestimate the skills you clearly have in pulling something like this off, unaided. Wouldn't it be interesting (or perhaps "scary" would be a better word) if "Montessori" steps could be / were recorded so we could learn how you did it?
You and DeeDee have another skill: you say things and create things that zero in on the needs, skills and interests of others. Gives one hope and faith.
For example: DeeDee's poast with the moovin' box and kitty and your follow-up remark about the moove. And what it will permit Max to do and be after it's complete.
And telling me I have certain skills.
Thanks.
It is nice we are all becoming REAL friends - I just love all of you!
It would take some time to recreate the steps in writing, and I may do it sometime, when I have the time, but now is not the time. I didn't save my grapsh-scraps, so I would have to do it all over again, but it won't take as long as I remember what I did. It would be a project all in itself! I think using your rods are similar to using the graph paper, except you were working 3 dimensional and I was working one dimensional - in either case, where there is a will there is a way.
"You and DeeDee have another skill: you say things and create things that zero in on the needs, skills and interests of others. Gives one hope and faith."
Why Tank u TcT:-) It's a wumin thing, I tink.
A minor point but ...
I did not solve this problem using Cuisenaire rods. I solved it with my program. I then took what my program told me the sides had to be and, using the diagram the program was based on, placed the appropriate rods in the appropriate places. These rods are perfect for this because their lengths are 1x1 up to 10x10.
I know you used the computer program and displayed your results with the rods, but I guess I meant to say, you could have used them, because they are, as you say, perfect dimensions for this particular puzzle.
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