Search found 10 matches

by pex
Mon Nov 12, 2018 9:04 am UTC
Forum: Logic Puzzles
Topic: Switch
Replies: 3
Views: 2202

Re: Switch

Yeah, if you actually put some thought into it, it's not that surprising any more. Good catch!
by pex
Sun Nov 11, 2018 8:11 am UTC
Forum: Logic Puzzles
Topic: Switch
Replies: 3
Views: 2202

Re: Switch

Well, there's the obvious solution:
Spoiler:
Press every LED once. Now all of them have been toggled three times, so if they started all off, they're now all on.
I assume this can be sped up, but, meh. Edit: brute force says it cannot, actually.
by pex
Fri Mar 09, 2018 8:15 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1964: "Spatial Orientation"
Replies: 77
Views: 16347

Re: 1964: "Spatial Orientation"

GlassHouses wrote:the western coast, i.e. pretty much the coast of Holland (as in: the provinces of North and South Holland, not its technically incorrect yet widely used meaning of the Netherlands as a whole)

Don't forget that North Holland also has an eastern coast. Which used to be on the Southern Sea.
by pex
Sat May 21, 2016 11:31 pm UTC
Forum: Mathematics
Topic: Meta-Probability Problem
Replies: 16
Views: 4676

Re: Meta-Probability Problem

Paradoxica wrote:As well as all the other functions that can be artificially constructed to be absolutely less than unity in domain but cover the entire real line in output.


gmalivuk wrote:But there's no motivation for any particular choice of adjustment


Might I suggest we pick the inverse of the normal CDF?
by pex
Sun Apr 10, 2016 3:33 am UTC
Forum: Mathematics
Topic: Efficient Prizims
Replies: 9
Views: 2558

Re: Efficient Prizims

Right, I was solving the wrong problem. First coffee, then post. Sorry.
by pex
Sun Apr 10, 2016 2:32 am UTC
Forum: Mathematics
Topic: Efficient Prizims
Replies: 9
Views: 2558

Re: Efficient Prizims

My intuition for why a half-cube is the most efficient shape for a box with no top:
Spoiler:
Place it on a mirror, upside down.
by pex
Tue Apr 05, 2016 1:01 pm UTC
Forum: Mathematics
Topic: Need help with non-linear Diophantine
Replies: 10
Views: 3157

Re: Need help with non-linear Diophantine

I am not near my notes (not even sure if they haven't been recycled yet), but as I recall, the bashing did involve some quadratic residues, modulo (stuff that is only positive for negative d). That is, I was explicitly looking for negative d only, since the case of positive d was completely settled ...
by pex
Tue Mar 29, 2016 2:15 am UTC
Forum: Mathematics
Topic: Need help with non-linear Diophantine
Replies: 10
Views: 3157

Re: Need help with non-linear Diophantine

[rambling] Long and boring case bashing (mod 8) seems to indicate that the only non-square d for which there might be solutions are d = 3-8k, for positive integers k. Warning: this result is based on lots of ugly scribbling which I don't feel like typing up since I feel there ought to be a more eleg...
by pex
Mon Mar 28, 2016 8:24 am UTC
Forum: Mathematics
Topic: Need help with non-linear Diophantine
Replies: 10
Views: 3157

Re: Need help with non-linear Diophantine

While my previous post was in the moderation queue, I noticed the same transformations mentioned by Cauchy: if (a,b,c,d) is a solution, then so are (b, bd-a, a, d) and (c, a, cd-a, d). This still doesn't help us understand for which values of d solutions exist, however. So far I have only found solu...
by pex
Mon Mar 28, 2016 4:09 am UTC
Forum: Mathematics
Topic: Need help with non-linear Diophantine
Replies: 10
Views: 3157

Re: Need help with non-linear Diophantine

I believe the general statement is "nonlinear Diophantine equations are hard". Let k be an arbitrary integer. The solution family that you found is (a,b,c,d) = (k, k 3 , 0, k 2 ); a couple of others are (0, k, -k, k 2 ) and (k 3 , k, k 5 -k, k 2 ), as well as (obviously) the same things wi...

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