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Author Topic:   puzzle (again)...

onepaul posted 06-14-99 12:34 PM ET

hmm...?
onepaul posted 06-14-99 01:39 PM ET
anyone...for 5 points!
4Horses posted 06-14-99 01:52 PM ET
Your a$$?
onepaul posted 06-14-99 01:56 PM ET
4whores, nope, that's -5 for you
Alphaman posted 06-14-99 01:57 PM ET
You gonna have to give more than 5 points before I even start thinking about that.
http://www.fortunecity.com/skyscraper/terabyte/607/bizare.gif
I will go here later and find the answer!
HA!
JohnIII posted 06-14-99 02:00 PM ET
What if he just uploaded the image to his webspace, not to his site?
John III
onepaul posted 06-14-99 02:02 PM ET
there is no answer at the site boys...
Alphaman posted 06-14-99 02:07 PM ET
Well then we are just going to have to storm off in a huff aren't we?
Anyway, even if we had an answer we have to descibe it in words which could take a while.
JohnIII posted 06-14-99 02:10 PM ET
Told you :p
John III
Smeagol posted 06-14-99 02:37 PM ET
Before I even begin to wonder over this, let me ask-- is this "puzzle" only in 2 dimensions? Obviously it appears that way, but I just want to make sure there aren't any unseen tricks going on here.
Smeagol posted 06-14-99 02:46 PM ET
My immediate answer is that the hole doesn't "come" from anywhere-- it just naturally exists in the second arrangement.
Rex Little posted 06-14-99 02:51 PM ET
The answer stems from the fact that neither of the two figures is actually a triangle! What looks like the hypotenuse in each case is actually two line segments, made up of the hypotenuse of the red triangle and that of the green triangle. Since these two have slopes that are almost, but not quite, identical (3/8 vs. 2/5), the "false hypotenuse" looks straight to the observer. In fact, it's slightly concave in the first figure and slightly convex in the second, and the difference is just enough to account for that one square.
Provost Harrison posted 06-14-99 02:53 PM ET
That's a damn good question, and the answer is:
Expected total surface area of the full shape (if triangle) would be 32.5 squares.
Same as bottom 32.5 squares.
Surface area of constituent triangles:
Red: 12 squares
Green: 5 squares
Surface area of constituent blocks
Orange: 7 blocks
Green: 8 blocks
Two blocks must compose a total surface area of 32.5-(12+5)=15.5 squares
However, area remaining for two blocks in the top one: 15 squares
bottom one: 16 squares
How is this possible, you may ask:
Because it isn't a goddam triangle if you look. It's a quadrilateral. And therefore they are both different shapes with differing areas: The top one is a quadrilateral with an internal area of 32 squares. The bottom one has a total surface area of 33 squares. The hypotenuses of both the triangles are joining in different patterns. The green one has a gradient of 2/5th and the red one a gradient of 3/8ths. Not the same gradient, therefore do not form a line. In the top one, it forms an inward bulging line due to the order (hence less area), in the bottom an outward bulge (hence larger surface area, and the remaining block).
Thankyou
Provost Richard Harrison M.Bioch (Hons) (Oxon)
Or to you, just GENIUS
And I didn't cheat, I did work that one out. But it is either a thing of close observation or geometry.
Provost Harrison posted 06-14-99 02:55 PM ET
Rex, I think we were both at about the same time. I was still writing before you posted.
JohnIII posted 06-14-99 02:55 PM ET
I was working that out, then got bored and played Quake 3.
Well done.
John III
Smeagol posted 06-14-99 05:47 PM ET
Wow-- I could have stared for hours, and I still wouldn't see that. I didn't consider that the gradients were different, when a quick mathematical treatment makes this obvious.
How carelessly stupid of me.
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Author	Topic: puzzle (again)...
onepaul	posted 06-14-99 12:34 PM ET hmm...?
onepaul	posted 06-14-99 01:39 PM ET anyone...for 5 points!
4Horses	posted 06-14-99 01:52 PM ET Your a$$?
onepaul	posted 06-14-99 01:56 PM ET 4whores, nope, that's -5 for you
Alphaman	posted 06-14-99 01:57 PM ET You gonna have to give more than 5 points before I even start thinking about that. http://www.fortunecity.com/skyscraper/terabyte/607/bizare.gif I will go here later and find the answer! HA!
JohnIII	posted 06-14-99 02:00 PM ET What if he just uploaded the image to his webspace, not to his site? John III
onepaul	posted 06-14-99 02:02 PM ET there is no answer at the site boys...
Alphaman	posted 06-14-99 02:07 PM ET Well then we are just going to have to storm off in a huff aren't we? Anyway, even if we had an answer we have to descibe it in words which could take a while.
JohnIII	posted 06-14-99 02:10 PM ET Told you :p John III
Smeagol	posted 06-14-99 02:37 PM ET Before I even begin to wonder over this, let me ask-- is this "puzzle" only in 2 dimensions? Obviously it appears that way, but I just want to make sure there aren't any unseen tricks going on here.
Smeagol	posted 06-14-99 02:46 PM ET My immediate answer is that the hole doesn't "come" from anywhere-- it just naturally exists in the second arrangement.
Rex Little	posted 06-14-99 02:51 PM ET The answer stems from the fact that neither of the two figures is actually a triangle! What looks like the hypotenuse in each case is actually two line segments, made up of the hypotenuse of the red triangle and that of the green triangle. Since these two have slopes that are almost, but not quite, identical (3/8 vs. 2/5), the "false hypotenuse" looks straight to the observer. In fact, it's slightly concave in the first figure and slightly convex in the second, and the difference is just enough to account for that one square.
Provost Harrison	posted 06-14-99 02:53 PM ET That's a damn good question, and the answer is: Expected total surface area of the full shape (if triangle) would be 32.5 squares. Same as bottom 32.5 squares. Surface area of constituent triangles: Red: 12 squares Green: 5 squares Surface area of constituent blocks Orange: 7 blocks Green: 8 blocks Two blocks must compose a total surface area of 32.5-(12+5)=15.5 squares However, area remaining for two blocks in the top one: 15 squares bottom one: 16 squares How is this possible, you may ask: Because it isn't a goddam triangle if you look. It's a quadrilateral. And therefore they are both different shapes with differing areas: The top one is a quadrilateral with an internal area of 32 squares. The bottom one has a total surface area of 33 squares. The hypotenuses of both the triangles are joining in different patterns. The green one has a gradient of 2/5th and the red one a gradient of 3/8ths. Not the same gradient, therefore do not form a line. In the top one, it forms an inward bulging line due to the order (hence less area), in the bottom an outward bulge (hence larger surface area, and the remaining block). Thankyou Provost Richard Harrison M.Bioch (Hons) (Oxon) Or to you, just GENIUS And I didn't cheat, I did work that one out. But it is either a thing of close observation or geometry.
Provost Harrison	posted 06-14-99 02:55 PM ET Rex, I think we were both at about the same time. I was still writing before you posted.
JohnIII	posted 06-14-99 02:55 PM ET I was working that out, then got bored and played Quake 3. Well done. John III
Smeagol	posted 06-14-99 05:47 PM ET Wow-- I could have stared for hours, and I still wouldn't see that. I didn't consider that the gradients were different, when a quick mathematical treatment makes this obvious. How carelessly stupid of me.