Search found 284 matches

Wed May 16, 2007 8:07 pm UTC
Forum: Coding
Topic: Does anyone here compete on Topcoder?
Replies: 30
Views: 14923
There's solved and 'solved'. There are LOTS of ways to 'solve' a problem, but a decent solution can be harder to find. Sort of like that 'OMGWTF' contest, you can satisfy the submission by simply sticking the correct operations into the stubbed out functions. That won't win, and it's not what the p...
Wed May 09, 2007 2:59 pm UTC
Forum: Logic Puzzles
Topic: Tic-tac-toe variant
Replies: 2
Views: 2192
If X goes first, O can make someone win with ease. X middle, O corner, X ?, O corner "check", X corner to block, now X has two in a line with the last space empty, O simply declines to place there and X must at the end. The same idea works for either of X's other starting moves. If X wins ...
Wed May 09, 2007 2:44 pm UTC
Forum: Mathematics
Topic: Trigonometry Joke
Replies: 15
Views: 7724
Yeah, the sin(theta) bit only makes sense to you because that's when you thought of it. Scratch that and just use the unit circle. Plus then your joke contains the word unit!!!!!!!
Thu May 03, 2007 4:17 pm UTC
Forum: Mathematics
Topic: The number i
Replies: 57
Views: 18322
Regarding i in physics, I don't know of anywhere in physics where you actually need i. It certainly is very useful, for example in quantum mechanics, but eventually, you only measure real numbers, and you an do all of the calculations using real numbers. Regarding real numbers in physics, I don't k...
Wed May 02, 2007 3:37 pm UTC
Forum: Mathematics
Topic: Duplicate Bananas
Replies: 37
Views: 8647
Pro Choice all the way. The universe is discrete and mathematics is better than it. This should have been a poll?
Mon Apr 30, 2007 12:48 pm UTC
Forum: Logic Puzzles
Topic: Chess Game [solution discussion]
Replies: 11
Views: 4897
Umm... I thought the original question stated that the checkmate move occurred on the 5th move of the game. The 5th move is taken by white, not black, and it's only his 3rd move of the game... seems impossible given the constraints. Okay, I admit that if you consider that a checkmate via knight cap...
Tue Apr 17, 2007 4:20 pm UTC
Forum: Logic Puzzles
Topic: A question more than a puzzle
Replies: 60
Views: 11614
bigglesworth wrote:That... wasn't the solution I was expecting.

Welcome to mathematics!
Fri Apr 13, 2007 3:43 pm UTC
Forum: Logic Puzzles
Topic: 12 marbles and a scale....kinda like 8
Replies: 15
Views: 4552
Yakk wrote:Yes!

We need some kind of fuzzy recognizer that says "it looks like this thread has been started several times before, perhaps you should check?"
Thu Apr 12, 2007 4:00 pm UTC
Forum: Logic Puzzles
Topic: Digits
Replies: 32
Views: 5728
The only way you're going to win on this one is when the amount of data given is so lengthy that the generative rule is simpler than the restatements that Yakk and I have given. Which isn't too hard; but it will take more than 6 data points. Actually it's very easy to 'win': Tally all of the thread...
Wed Apr 11, 2007 11:47 pm UTC
Forum: Logic Puzzles
Topic: Digits
Replies: 32
Views: 5728
Nei'hoor. Probably, for some value of L(7), I can find a polynomial with rational coefficients that is information-theoretically simpler than the string "the number of letters present in the shortest English description of x." Not to mention that each of those sub-objects is infinitely mo...
Tue Apr 10, 2007 4:11 am UTC
Forum: Logic Puzzles
Topic: Digits
Replies: 32
Views: 5728
Just be careful with your equals signs, dude. It would have been better to say something like, L(1) = 3 L(2) = 3 L(3) = 5 L(4) = 4 L(5) = 4 L(6) = 3 What is L(7)? The problem, of course, is that I can construct a polynomial that has the proper L(i) for each i given, and has whatever L(7) I want it ...
Mon Apr 09, 2007 9:38 pm UTC
Forum: Logic Puzzles
Topic: Digits
Replies: 32
Views: 5728
R=arrr

Depending one how it actually works, either:

-2=12=6=3=5=4=4=4=4...
or
-2=11=6=3=5=4=4=4=4...
Mon Apr 09, 2007 9:15 pm UTC
Forum: Logic Puzzles
Topic: Two numbers
Replies: 20
Views: 4216
LE4dGOLEM wrote:
Drostie wrote:Yes, there are.

0 * 0 = 0.0

Done.

Only works because he didn't say "Integer"

Are you claiming that 0 is not an integer or mistaking Drostie's post as an answer to Dingos' instead of an answer to HYPERiON's?
Mon Apr 09, 2007 9:12 pm UTC
Forum: Logic Puzzles
Topic: Digits
Replies: 32
Views: 5728
By transitivity, even relaxing commutivity, isn't it the case that for any number R, R=4?
Tue Apr 03, 2007 10:50 pm UTC
Forum: Logic Puzzles
Topic: Is this a question?
Replies: 41
Views: 8608

Re: Is this a question?

aarestad wrote:It's not even a sentence.

Why not? Wasn't that? Do you subscribe to a strange, restrictive definition of sentence with requirements divorced from actual practice?

There, there.
Wed Mar 21, 2007 7:21 pm UTC
Forum: Logic Puzzles
Topic: Simplified luring lottery [solutions discussion]
Replies: 12
Views: 3829
What if there are no best strategies? (or, no best strategy which can be deduced rationally, for you non-construtive logicians) What if there is a continuum of best strategies? What if there is a non-compact subset of R of best strategies? Take the game "highest number". Pick a number rea...
Wed Mar 21, 2007 5:12 pm UTC
Forum: Logic Puzzles
Replies: 9
Views: 4030
I win the prize for least time spent to feel confident of a 50% chance at the right answer?
Wed Mar 21, 2007 4:53 pm UTC
Forum: Logic Puzzles
Topic: Simplified luring lottery [solutions discussion]
Replies: 12
Views: 3829
To maximize the expected value of the prize, I tried differentiating the expected value and setting that equal to zero. Surprisingly something nice popped out, maybe someone should check my work: 1-(1-p)^N = N*p*E(p) where E(p) is the expected value of the prize (U=1) if everyone enters with probabi...
Wed Mar 21, 2007 4:48 pm UTC
Forum: Logic Puzzles
Topic: Simplified luring lottery [solutions discussion]
Replies: 12
Views: 3829
However, stating that this can be deduced by invoking "perfect rationality" is a bit of a stretch. :) Not much of a stretch, really. Suppose there is exactly one best strategy, then everyone will choose it, and all strategies are expressible by "enter with probability p". If the...
Wed Mar 21, 2007 2:47 pm UTC
Forum: Logic Puzzles
Topic: Simplified luring lottery [solutions discussion]
Replies: 12
Views: 3829
Yakk wrote:The two person case in the original post seems to have problems.

Remember that if two people enter, the prize given out is only U/2, not U.
Tue Mar 20, 2007 11:17 pm UTC
Forum: Logic Puzzles
Replies: 9
Views: 4030

Two non-adjacent edges... Okay, from an edge to a vertex is a bit longer, and from a vertex to a vertex a bit longer, so we'll estimate the side length to be 1.5 * 6 = 9. Then the base (one triangle) is area about 9*9sqrt(2)/2, which we'll say is like 81*3/4~=60. A cube with that base would be about...
Tue Mar 20, 2007 7:50 pm UTC
Forum: Logic Puzzles
Topic: Simplified luring lottery [solutions discussion]
Replies: 12
Views: 3829

Re: Simplified luring lottery [solutions discussion]

Those were similar to my lines of thought. In fact we may be able to extract something nice if we can simplify your expected value expression: (C(N,1)*p*q^(N-1)+(1/2)*C(N,2)*p^2*q^(N-2)+(1/3)*C(N,3)*p^3*q^(N-3)+...+(1/n)*C(N,N)*p^N) =sum((1/k)*C(N,k)*p^k*(1-p)^(N-k),k=1..N) This is very close to a s...
Tue Mar 20, 2007 3:42 pm UTC
Forum: Logic Puzzles
Topic: Simplified Luring Lottery
Replies: 1
Views: 2266

Simplified Luring Lottery

First assume superrationality, the idea that everyone knows that everyone knows that (etc) everyone is perfectly rational. Thus everyone ends up with the same strategy. Also assume no communication between participants. Here's the puzzle: I offer a prize of utility U to N of you. Your choices are a)...
Wed Feb 28, 2007 1:17 am UTC
Forum: Logic Puzzles
Topic: Donuts Revisited
Replies: 4
Views: 2558
A good Bayesian, whether or not he knows anything about those distributions or the distribution of possible initial donut stack probabilities, will assign priors to them anyway.
Wed Jan 31, 2007 4:06 am UTC
Forum: Logic Puzzles
Topic: Riddle I Came Up With- No Maths Required!
Replies: 29
Views: 8404

"To do this, remove the jaw from the wrench and grind one more notch on the â€œrackâ€
Fri Jan 19, 2007 5:23 pm UTC
Forum: Logic Puzzles
Topic: Official xkcd puzzle [solution]
Replies: 14
Views: 5099
Erasmus wrote:I would have called that "inductive reasoning" -- obviously such integer-sequence problems, like science, suffer from the problem of induction -- but to each his own.

I'd say definitely not to each his own. It's inductive reasoning, like pretty much all of science, not deductive.
Fri Jan 12, 2007 3:24 am UTC
Forum: Logic Puzzles
Topic: pentagons inside of a triangle
Replies: 14
Views: 4389
skeptical scientist wrote:
I have a nicely symmetrical way of doing it with 9.

I'm guessing it's the same as mine then.
Fri Jan 12, 2007 12:56 am UTC
Forum: Logic Puzzles
Topic: pentagons inside of a triangle
Replies: 14
Views: 4389
bitwiseshiftleft wrote:I can do it with
10
I won't post the solution until I can improve it or prove that it's minimal.

I've got
9
Tue Jan 09, 2007 12:23 am UTC
Forum: Logic Puzzles
Topic: [Solution] #6: Footsteps on the Tile
Replies: 5
Views: 2877
rhino wrote:Or:
1:1, because there are countably infinitely many red squares, and countably infinitely many grey squares. Not only that, there are also countably infinitely many white squares, so the ratio white:red:grey is 1:1:1.

Instead use natural density or something.
Tue Jan 09, 2007 12:21 am UTC
Forum: Logic Puzzles
Topic: #13: Them Speedy Steppe Flies
Replies: 19
Views: 6026

Re: #13: Them Speedy Steppe Flies

A fly is doomed to meet its gristly end between two very large trains in a very small tunnel. The two trains start at different ends of a 100 mile tunnel and move toward eachother each going 25 mph. The fly starts from one of the trains the instant it starts moving and can accelerate (and decelerat...
Mon Jan 08, 2007 4:49 pm UTC
Topic: 0207: "What xkcd Means"
Replies: 482
Views: 75038
I wonder how far in the busy beaver sequence you have to go to pwn A(g_64, g_64). The 100th is with all likelihood enough. Maybe even the 50th, 20th or maybe 10th. Ooh, I was just going to mention that. In the circles I run we a) call the busy beaver function of n "BB(n)", and b) express ...
Wed Dec 20, 2006 4:13 am UTC
Forum: Logic Puzzles
Topic: [Solution] #6: Footsteps on the Tile
Replies: 5
Views: 2877
Or, without visualizing anything... Each set of 4 gray has 1 red, but each gray is used in 4 sets.
Wed Dec 13, 2006 6:34 am UTC
Forum: Logic Puzzles
Topic: Infinite hats
Replies: 31
Views: 12375
Gotcha. Now I agree.
Tue Dec 12, 2006 8:06 pm UTC
Forum: Logic Puzzles
Topic: Infinite hats
Replies: 31
Views: 12375
Maybe it's just a matter of semantics, but I would say a strategy does exist (albeit an unusable one). Putting everything into a mathematical setting -- Let S be the set of all the logicians, h be an arbitrary function from S to {red,blue}, and R the set of all elements s in S such that h(s)=red. W...
Tue Dec 12, 2006 5:30 pm UTC
Forum: Logic Puzzles
Topic: Infinite hats
Replies: 31
Views: 12375
So there exists a strategy, but I doubt they can actually find it, given the non-constructive nature of the Axiom of Choice. I guess the question remains as to whether anyone can find a strategy, rather than just proving its existence. Surely a strategy that they can't actually use isn't actually a...
Tue Dec 12, 2006 3:34 am UTC
Forum: Logic Puzzles
Topic: Infinite hats
Replies: 31
Views: 12375
Pick number Check if number results in finitely many differences If it does, pick it, yell out choice If it doesn't, pick next number and repeat The only problem I see here, and the reason I almost didn't submit this, is that each logician is required to do potentially infinite work. This doesn't w...
Mon Dec 11, 2006 11:28 pm UTC
Forum: Logic Puzzles
Topic: Sum of two sequences
Replies: 2
Views: 2388

Re: Sum of two sequences

BaldAdonis wrote:2, 3, 6, 14, 40, 152, 784, ...

OEIS agrees.
Mon Dec 11, 2006 12:27 pm UTC
Forum: Logic Puzzles
Topic: Official xkcd puzzle [SOLUTIONS]
Replies: 47
Views: 83381
I must admit I cannot rationalize F(34)=55 and F(35)=53. If those really are the correct values, I submit that my sequence F' is nicer, and more in keeping with the newly revealed comic (which is now outside my office). For 0<=x<=33 and x=71, F'(x)=F(x), but F'(34)=51 and F'(35)=49. F'(x) for 36<=x<...
Sun Dec 10, 2006 1:17 am UTC
Forum: Logic Puzzles
Topic: Envelopes puzzle
Replies: 10
Views: 6104
That x doesn't remain constant? Sure it does. If you like, open the first envelope. Say it contains \$100. Now should you switch? Same logic: 50% chance the other contains \$50, 50% chance it contains \$200. So by switching you get expected value \$50/2 + \$200/2 = \$125. But you'd have come to that conc...
Tue Nov 28, 2006 11:52 pm UTC
Forum: Logic Puzzles
Topic: An Interesting Hypothesis [solution thread]
Replies: 1
Views: 2108