# 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.

Author Message
Lepton
1:41+ Arse Scratcher

 Posted: Fri Mar 08, 2002 4:09 am    Post subject: 1 a^2 + b^2 = c^2 3^2 + 4^2 = 5^2 .......Everyone knows Pythagores' Theorem. a^3 + b^3 + c^3 = d^3 3^3 + 4^3 + 5^3 = 6^3 ........Fancy, eh? What does d^3 signify? (I don't know the answer myself)
Chuck
Daedalian Member

 Posted: Fri Mar 08, 2002 4:54 am    Post subject: 2 Mere coincidence. It means nothing.
Bicho the Inhaler
Daedalian Member

 Posted: Fri Mar 08, 2002 4:59 am    Post subject: 3 "There are no coincidences in the natural numbers." or something to that effect, said by someone or other famous.
daniel801
Daedalian Member

 Posted: Fri Mar 08, 2002 5:12 pm    Post subject: 4 it means that three ice cubes of sides 3, 4, and 5 when melted would fit in an ice cube tray with side 6
daniel801
Daedalian Member

 Posted: Fri Mar 08, 2002 6:51 pm    Post subject: 5 ...if re-frozen
Lepton
1:41+ Arse Scratcher

 Posted: Sat Mar 09, 2002 4:36 am    Post subject: 6 But no funky trigangle-y goodness?
groza528
No Place Like Home

 Posted: Sat Mar 09, 2002 7:31 am    Post subject: 7 Not that I know of (displays title)
Suspence
Daedalian Member

 Posted: Sat Mar 09, 2002 3:05 pm    Post subject: 8 I found the quote to which Mr. Inhaler refers: "Achilles: An "infinite coincidence"? Among the natural numbers, NOTHING is coincidental-nothing happens without there being some underlying pattern. " It has to mean something somewhere...but what??? ------------------ I hate people who try to write interesting things in their signature
Bicho the Inhaler
Daedalian Member

 Posted: Sat Mar 09, 2002 6:19 pm    Post subject: 9 Yes, page 398 of Hoftstadter's GEB. That must have been it.
Coyote

 Posted: Sat Mar 09, 2002 10:37 pm    Post subject: 10 http://mathforum.org/dr.math/problems/toscano7.14.97.html I don't really understand why Fermat's Last Theorem being proven implies that no formula for finding solutions to a^3+b^3+c^3=d^3 exists, but if it's true, I doubt there'll be any 'practical' application similar to the Pythagorean Theory. The article lists several other solutions to the equation though, just in case anyone wants to look them over and try to figure out some kind of connecting idea to them.
dave10000
Tinhorn

 Posted: Sun Mar 10, 2002 5:06 am    Post subject: 11 For no good reason, I wrote the following Mathematica program: While[ (a = Random[Integer, {1000, 1500}]) || (b = Random[Integer, {1000, 1500}]) || (c = Random[Integer, {1000, 1500}]) || !IntegerQ[(a^3 + b^3 + c^3)^(1/3)]] Print[a] Print[b] Print[c] Print[(a^3 + b^3 + c^3)^(1/3)] In under 2 minutes of run time, my computer told me that: 1004^3 + 1219^3 + 1332^3 = 1731^3
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year by All usersBicho the InhalerChuckCoyotedaniel801dave10000groza528LeptonSuspence Oldest FirstNewest First
 All times are GMT Page 1 of 1

 Jump to: Select a forum Puzzles and Games----------------Grey Labyrinth PuzzlesVisitor Submitted PuzzlesVisitor GamesMafia Games Miscellaneous----------------Off-TopicVisitor Submitted NewsScience, Art, and CulturePoll Tournaments Administration----------------Grey Labyrinth NewsFeature Requests / Site Problems
You cannot post new topics in this forum
You can reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum