# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

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zorT Kitty
Oboe! Another bassoonist!

 Posted: Wed Nov 05, 2003 2:34 am    Post subject: 1 http://www.ebaumsworld.com/trigrid.html I can't seem to figure this one out. There's a slight difference in angles, and I dont think they form 2 big triangles and rather form quadrilaterals, but it doesn't seem enough to compensate for the empty box. At 9:30 it's past my bedtime and I can't think clearly, so if you can help it'd be greatly appreciated.
Beartalon
'Party line' kind of guy

 Posted: Wed Nov 05, 2003 2:38 am    Post subject: 2 In order for this initial triangle to exist, the red and green must be similar. The ratio of non-hypoteneuse sides for the green is 2/5. The ratio of non-hypoteneuse sides for the red is 3/8. Because 2/5 <> 3/8, the first triangle is NOT a real triangle, it just looks close, and it lets them pull of the missing square trick. [This message has been edited by Beartalon (edited 11-04-2003 09:39 PM).]
Lilifreid
DANGER!

 Posted: Wed Nov 05, 2003 2:44 am    Post subject: 3 The slope on the red triangle is 3/8, or 15/40. The slope on the green triangle is 2/5, or 16/40. So, neither assembly of pieces forms a true triangle. The "hypotenuse" on the top assembly is slightly concave, while the "hypotenuse" on the lower assembly is slightly convex.
Lilifreid
DANGER!

 Posted: Wed Nov 05, 2003 2:49 am    Post subject: 4 Sorry, I typed slow.
Mercuria
Merc's Husband's Wife!

 Posted: Wed Nov 05, 2003 2:58 am    Post subject: 5 it's okay, we don't think you copied the answer or anything =]
Kazooish
The Moofin Man

 Posted: Wed Nov 05, 2003 3:21 am    Post subject: 6 long time no hear from me...its me who was talking to katie about this... i made my own....which definitly started as a triangle...and definitly appeared as a triangle afterwords, with the extra square there....maybe my second configuration wasnt ar eal triangle...but at least one of them is.
Lilifreid
DANGER!

 Posted: Wed Nov 05, 2003 3:24 am    Post subject: 7 What do you mean, made your own? Drawn or cut out? Either technique has a large enough margin of error that it will still look to work out as in the picture.
Lilifreid
DANGER!

 Posted: Wed Nov 05, 2003 3:27 am    Post subject: 8 Think of it this way: If you construct a right triangle that has a leg 5 units long and a leg 13 units long, will the hypotenuse ever exactly intersect a lattice point on the grid? [This message has been edited by Lilifreid (edited 11-04-2003 10:28 PM).]
Bicho the Inhaler
Daedalian Member

 Posted: Wed Nov 05, 2003 4:08 am    Post subject: 9 Here's yet another thing to notice: the area of a right triangle with legs 5 and 13 is 65/2 = 32.5, but the sum of the areas of the colored shapes is 32, which is almost, but not quite, 32.5. This should tell you that something in the drawing is only approximate. (As others have pointed out, the "hypotenuse" is not exactly straight.)
zorT Kitty
Oboe! Another bassoonist!

 Posted: Thu Nov 06, 2003 3:06 am    Post subject: 10 cool. thanks. it all makes sense now! wow. what a novelty.
Macros
Daedalian Member

 Posted: Thu Nov 06, 2003 7:52 pm    Post subject: 11 i think the GL coulld do with a section of optical illusions, for younger puzzlers and the stupider people (me) i think it was mentioned before
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