MC: 4th power with no small digits
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From: Joe Horn on 23 Mar 2010 19:42 > Presuming that you have already found one such integer, do you have a > proof that there cannot be more than one? I have no proof that the known solution is the only solution, nor do I have a proof that another solution exists. A fast PC (Intel Core i5 750 @ 2.67 GHz) running 4 parallel loops failed to find another solution after several hours; ergo, if another solution exists, it is extremely large. None of this has anything to do with the mini- challenge, although it is stimulating in its own right as a math problem. Did you know that X^12 always contains a 0 or a 1? But I digress. > If not, I suggest that you ask for a program which finds the smallest > such integer. Or we can go the other direction and simply ask for ANY solution, whether smallest or not. Whatever. It only matters if other solutions actually exist, which the Achilles in me tends to doubt. (cf. "Gödel, Escher, Bach") -Joe-
From: Han on 23 Mar 2010 19:42 On Mar 23, 7:25 pm, Jim Horn <jamesludwigh...(a)gmail.com> wrote: > Well, Excel makes it easy to search manually, giving me 0xB34 in short > order. I know, that doesn't count. Gotta keep my HP50g where I can > get at it (or put a programming language on my work laptop). > > Where *do* you come up with these interesting problems, anywho? > > Jim (Why the Hex answer? Don't want to give it entirely away for > those who want to solve it themselves) My HP 49G+ just confirmed Jim's answer. Using TIME and HMS-: 0.0429166382 (just under 4.5 minutes). I'm working on improving the algorithm. Let's see how quickly this time is destroyed. =)
From: Joe Horn on 23 Mar 2010 19:48 > Where *do* you come up with these interesting problems, anywho? Tumbolia, the place where hiccups go when they go away. ;-) -Joe-
From: Han on 23 Mar 2010 20:19 > My HP 49G+ just confirmed Jim's answer. Using TIME and HMS-: > 0.0429166382 (just under 4.5 minutes). I'm working on improving the > algorithm. Let's see how quickly this time is destroyed. =) Current speed: 0.0256074341 (2 minutes 56 seconds)
From: Jim Horn on 23 Mar 2010 20:23
On Mar 23, 4:48 pm, Joe Horn <joeh...(a)holyjoe.net> wrote: > > Where *do* you come up with these interesting problems, anywho? > > Tumbolia, the place where hiccups go when they go away. ;-) > > -Joe- Uh, as I recall, one of the GEB dialogs refers to Tumbolia as the destination of lost / mismatched socks. Those two ingredients lead to a disquieting mental image... |