Search found 602 matches

by Cauchy
Sat May 28, 2016 4:40 am UTC
Forum: Logic Puzzles
Topic: Logic Grid Puzzle - Cricket SOLUTION
Replies: 2
Views: 2808

Re: Logic Grid Puzzle - Cricket SOLUTION

Done. This wasn't particularly challenging, even though I know nothing about cricket.
by Cauchy
Wed May 25, 2016 10:08 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 80590

Re: Misunderstanding basic math concepts, help please?

Now that I know for certain that all mathematical propositions relating to axiomatic mathematics are excluded middle (unless explicitly noted otherwise); I need to find out whether this is as damaging to axiomatic mathematics as I think it is. I hear you loud and clear, Treatid. You've given up pre...
by Cauchy
Wed May 25, 2016 1:06 am UTC
Forum: Logic Puzzles
Topic: Open puzzle about game
Replies: 36
Views: 7766

Re: Open puzzle about game

I don't think anyone was saying that Build C is unbeatable. At least, I hope not, because I already pointed out that Build A beats it. In general, Goahead, I think you're misunderstanding what we're doing. The Builds we're proposing aren't suggestions for the unbeatable build. Rather, they're obstac...
by Cauchy
Wed May 25, 2016 12:24 am UTC
Forum: Mathematics
Topic: Is math real?
Replies: 105
Views: 20289

Re: Is math real?

I mean yes it's clear that under that definition math is not real. There's no a debate to be had there. Would anyone in this thread disagree with the statement that math is NOT real under that definition of real? I'm pretty sure that PsiCubed was arguing that under that definition, math *is* real, ...
by Cauchy
Tue May 24, 2016 5:21 pm UTC
Forum: Logic Puzzles
Topic: Open puzzle about game
Replies: 36
Views: 7766

Re: Open puzzle about game

@Cauchy Assume that at the turn 12 you have this situation : - It is the turn of Player 2 - Player 1 has still 1 piece 1x1. Player 1 has played (turn 11). He has the 12th turn remaining - The board 14x14 is not full yet. If you rearrange the board 14x14 you obtain a remaining square empty of mxm re...
by Cauchy
Tue May 24, 2016 4:19 pm UTC
Forum: Mathematics
Topic: Is math real?
Replies: 105
Views: 20289

Re: Is math real?

But anyways, I just want to say it doesn't seem like you're all really discussing whether math is real. Rather, you're discussing what you mean by real. Of course? This discussion was always going to mostly be about the definitions of "math" and "real". Once you have those, it's...
by Cauchy
Tue May 24, 2016 12:24 am UTC
Forum: Logic Puzzles
Topic: Open puzzle about game
Replies: 36
Views: 7766

Re: Open puzzle about game

(or is there a physically possible shape for a 4+ piece that doesn't allow the placement of 2 2x1?) The size 4 T-block from Tetris and the size 5 + sign both have this property. I think they're the only two. That second limitation isn't quite right. For example a set with zero 1-pieces and lots of ...
by Cauchy
Mon May 23, 2016 3:02 pm UTC
Forum: Logic Puzzles
Topic: Open puzzle about game
Replies: 36
Views: 7766

Re: Open puzzle about game

Here's a set that's guaranteed a win if it goes second. Cut off a 2-by-2 square from the corner of your 10-by-10 grid, and then cut a 1-by-1 square off of that to make a size 1 piece and an L-shaped size 3 piece. Cut the remaining 96 squares into ten pieces that reassemble to form the shape of a 14-...
by Cauchy
Sun May 22, 2016 10:42 pm UTC
Forum: Logic Puzzles
Topic: Open puzzle about game
Replies: 36
Views: 7766

Re: Open puzzle about game

Since the players have to place in an alternating fashion and the first player has to start with one of their smallest pieces, does that mean that the players have to play their pieces in size from smallest to largest as well? It sounds like you're making that assumption, but I don't see it anywhere...
by Cauchy
Thu May 19, 2016 11:40 pm UTC
Forum: Mathematics
Topic: Is math real?
Replies: 105
Views: 20289

Re: Is math real?

Gravity is totally a model! Or rather, Aristotelian gravity is a shit model, Newtonian gravity is a much better model, Einsteinian gravity is the most primo shit we got. You indeed named three models of gravity. That makes those things models, but not necessarily gravity itself. If you have names f...
by Cauchy
Thu May 19, 2016 1:47 pm UTC
Forum: Mathematics
Topic: Is math real?
Replies: 105
Views: 20289

Re: Is math real?

Gravity" describes some set of things in the universe. "Math" goes deeper, and attaches quantities and relations to those things (when it's used to talk about the real world). Both are obviously abstractions, but my line for "what counts as real" puts them on different side...
by Cauchy
Thu May 19, 2016 3:14 am UTC
Forum: Mathematics
Topic: Is math real?
Replies: 105
Views: 20289

Re: Is math real?

There's a distinction between "gravity" and "the current scientific model of gravity". I can't directly observe that the earth goes around the sun instead of vise versa, and I can't directly observe that clocks up in satellites go faster than clocks down here. I can observe thing...
by Cauchy
Sat May 14, 2016 9:07 pm UTC
Forum: Mathematics
Topic: Meta-Probability Problem
Replies: 16
Views: 4777

Re: Meta-Probability Problem

I read the question as "All you know about the distribution is that it's biased towards heads.". If you want to bring other "knowledge" into this about intuitions regarding coin manufacturing and whatnot, then that opens a can of worms that can't be sealed again. How do we know i...
by Cauchy
Sat May 14, 2016 5:54 am UTC
Forum: Mathematics
Topic: Meta-Probability Problem
Replies: 16
Views: 4777

Re: Meta-Probability Problem

If you know nothing about the coin other than that it's biased towards heads, then the probability distribution for the coin is 2 on [0.5, 1] and 0 everywhere else. The probability of a heads and a tails given a probability of heads p is 2p(1-p), so we get that the probability is int_{0.5}^1 2(2p(1-...
by Cauchy
Wed May 11, 2016 10:49 pm UTC
Forum: Mathematics
Topic: Seemingly simple
Replies: 16
Views: 4026

Re: Seemingly simple

We found out in Post 3 that another question (maybe even the more pertinent one) was "I'm building a roof, and I'm afraid of being off a few millimeters if I try to eyeball the answer to this problem. Help?". That's a question which GeoGebra is perfectly suited to answering, so the dismiss...
by Cauchy
Tue May 10, 2016 8:20 am UTC
Forum: Mathematics
Topic: Seemingly simple
Replies: 16
Views: 4026

Re: Seemingly simple

C/x = B/sqrt(B^2 -(A-x)^2) This should be C/x = B/sqrt(B^2 + (A-x)^2), since sqrt(B^2 + (A-x)^2) is the length of the hypotenuse of the large right triangle. Then, C sqrt(B^2 + (A-x)^2) = B x C^2 (B^2 + (A-x)^2) = B^2 x^2 B^2 C^2 + A^2 C^2 - 2 A C^2 x + C^2 x^2 = B^2 x^2 0 = (B^2 - C^2) x^2 + (2 A ...
by Cauchy
Fri May 06, 2016 6:32 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 80590

Re: Misunderstanding basic math concepts, help please?

What do "rigorously defined" and "unambiguous" mean when you use them, Treatid? What is "Axiomatic Mathematics"? What are "binary" and "continuous systems"? When you say "Axiomatic Mathematics must not be an excluded middle with respect to the p...
by Cauchy
Wed May 04, 2016 8:57 am UTC
Forum: Logic Puzzles
Topic: Logic Grid Puzzle!
Replies: 2
Views: 2933

Re: Logic Grid Puzzle!

Does anything of interest happen in this puzzle? All of the information given is positive, so it just sounds like setting out all of the various fragments, and then seeing which ones are forced to connect to which other ones. It'll be an exercise in tedium given the number of types and volume of inf...
by Cauchy
Fri Apr 22, 2016 10:25 pm UTC
Forum: Mathematics
Topic: Pi from the Menger Sponge
Replies: 9
Views: 4860

Re: Pi from the Menger Sponge

You're right, philip. I had got it into my head that you remove 1/(2n+1)^d of the measure each step, but that obviously can't be right since that's a decreasing function of d, and more needs to be removed as d increases, since the ratio of the measures of a d-ball and the d-cube that contains it dec...
by Cauchy
Thu Apr 21, 2016 9:14 pm UTC
Forum: Mathematics
Topic: Pi from the Menger Sponge
Replies: 9
Views: 4860

Re: Pi from the Menger Sponge

I'd like to point out that the formula doesn't work for n = 1. The length of a 1-dimensional unit ball is 2, but the length of the 1-sponge is 2*[2/3*4/5*6/7*...], which is decidedly less than 2 (since it's 0).
by Cauchy
Sat Apr 09, 2016 6:07 pm UTC
Forum: Mathematics
Topic: Efficient Prizims
Replies: 9
Views: 2591

Re: Efficient Prizims

Here's another way to see that s = 4 is the correct answer; this involves a bit of trickery and a smidgen of intuition. If we cut out four s-by-s squares from the corners and fold up, we see that we get an s-by-(24-2s)-by-(24-2s) box. As such, its volume is V = s(24-2s)^2. We wish to maximize V. Her...
by Cauchy
Tue Apr 05, 2016 8:39 am UTC
Forum: Mathematics
Topic: Simplifying expressions with unit'd values
Replies: 13
Views: 3672

Re: Simplifying expressions with unit'd values

You can always reduce any complex expression to the ratio of two polynomials, but you won't be able to go further than that, except in the case that the numerator and denominator share a common factor, or in the case that the denominator is a monomial.
by Cauchy
Mon Mar 28, 2016 11:10 pm UTC
Forum: Mathematics
Topic: Need help with non-linear Diophantine
Replies: 10
Views: 3212

Re: Need help with non-linear Diophantine

Thank you both for the help! Looks like I'm in over my head on this problem. You guys offered much need insight. Cauchy, the reformulation you mentioned was indeed an IMO problem. In fact, it showed up on Wikipedia's Vieta Jumping page! The IMO problem only asked for a proof that d is a perfect squ...
by Cauchy
Mon Mar 28, 2016 6:16 am UTC
Forum: Mathematics
Topic: Need help with non-linear Diophantine
Replies: 10
Views: 3212

Re: Need help with non-linear Diophantine

c+b = a*d c*b = a^2 - d c = ad - b (ad - b)b = a^2 - d abd - b^2 = a^2 - d abd + d = a^2 + b^2 d(ab+1) = a^2 + b^2 So ab+1 divides a^2 + b^2. I'm pretty sure I've seen "Find all pairs of integers (m, n) such that (m^2+n^2)/(mn+1) is an integer" as an Olympiad-level problem before, but I ca...
by Cauchy
Tue Mar 08, 2016 5:16 am UTC
Forum: Logic Puzzles
Topic: Logic puzzles beta testing
Replies: 4
Views: 2868

Re: Logic puzzles beta testing

Write-o. An c mutated into an e across four iterations of copying.
by Cauchy
Mon Mar 07, 2016 4:44 pm UTC
Forum: Logic Puzzles
Topic: Logic puzzles beta testing
Replies: 4
Views: 2868

Re: Logic puzzles beta testing

The answer to the puzzle you posted is
Spoiler:
hypodermie
by Cauchy
Sun Feb 21, 2016 10:34 am UTC
Forum: Logic Puzzles
Topic: Two gold nugget puzzle
Replies: 17
Views: 5463

Re: Two gold nugget puzzle

I can do it in eighteen weighings, but I don't have a proof that that's optimal. I also can't determine whether it could beneficial to weigh more than one nugget on a side in any cases.
by Cauchy
Sun Feb 21, 2016 12:03 am UTC
Forum: Logic Puzzles
Topic: Another smullyanesque puzzle
Replies: 14
Views: 4608

Re: Another smullyanesque puzzle

From David's statement, Cecilia is a knight. From Cecilia's statement, Cecilia's spouse is a knight. Therefore, Cecilia and her spouse are both knights. From Betty's statement, Adam and Betty have the same occupation. From Adam's statement, Adam and his spouse have different occ...
by Cauchy
Fri Feb 19, 2016 6:20 am UTC
Forum: Logic Puzzles
Topic: Anyone interested in a tough 5-question challenge?
Replies: 27
Views: 6320

Re: Anyone interested in a tough 5-question challenge?

Your question 3 doesn't appear in OEIS, so I don't know how anyone would get it. 2,3,6,9,36,41,246... doesn't appear in OEIS either yet it obviously has a unique correct answer (can anybody here figure out what it is?) That's only because you started with the wrong first term. https://oeis.org/A047...
by Cauchy
Wed Feb 17, 2016 3:25 pm UTC
Forum: Logic Puzzles
Topic: Anyone interested in a tough 5-question challenge?
Replies: 27
Views: 6320

Re: Anyone interested in a tough 5-question challenge?

Looking at the website confirms my suspicions: there's just not enough to go on in any of these questions. Any answer I came up with would be a shot in the dark, only correct on the off chance that I happened to think of the exact same thing that you did. Your question 3 doesn't appear in OEIS, so I...
by Cauchy
Tue Feb 16, 2016 4:19 am UTC
Forum: Logic Puzzles
Topic: Anyone interested in a tough 5-question challenge?
Replies: 27
Views: 6320

Re: Anyone interested in a tough 5-question challenge?

I'm not averse, but that particular question doesn't sound very interesting.
by Cauchy
Tue Feb 16, 2016 4:16 am UTC
Forum: Mathematics
Topic: Combinatorics : Castle, rooms and doors
Replies: 14
Views: 3260

Re: Combinatorics : Castle, rooms and doors

I tried to make a connection between 3-colorings and doors, using the colors at the corners and the vertices between the colors as walls. The numbers match but I don't see an intuitive connection yet. I'm pretty sure I see the connection. If we number the colors 1, 2, and 3, then traversing around ...
by Cauchy
Mon Feb 15, 2016 12:28 am UTC
Forum: Mathematics
Topic: Quadratic Reciprocity
Replies: 3
Views: 1817

Re: Quadratic Reciprocity

Since it is a law of numbers, it must be possible to see its mechanism through numbers alone. This is not true for the more advanced parts of number theory. The majority (the vast majority, probably) of semi-recent number theory breakthroughs have involved analyzing the structure of the integers th...
by Cauchy
Mon Feb 15, 2016 12:12 am UTC
Forum: Logic Puzzles
Topic: Unknown Digits
Replies: 6
Views: 2513

Re: Unknown Digits

(Coincidentally, it's immediately apparent that U = 1 from this and its first expression, but we don't need to use that fact for anything.) We can get to a faster contradiction using it. Since U = 1, D5 - D3 - D2 = 1, and so D5 = D2 + D3 + 1. Setting the two expressions for Q equal to each other, w...
by Cauchy
Mon Feb 08, 2016 3:53 pm UTC
Forum: Mathematics
Topic: Coin flip problem
Replies: 6
Views: 1921

Re: Coin flip problem

n is a fixed number of flips, namely the predetermined length of the run of coin flips you will do, as mentioned in the OP. Somehow, between reading the question and getting to Nitrodon's explanation, I forgot that there was a predetermined, finite number of flips, and then his use of "The pro...
by Cauchy
Sun Feb 07, 2016 12:58 pm UTC
Forum: Logic Puzzles
Topic: Russian Roulette with multiple cartridges
Replies: 4
Views: 3223

Re: Russian Roulette with multiple cartridges

Let A and B be the consecutive chambers that are fired when the trigger is pulled the first and second time, respectively. The question is: Given that chamber A is empty, what is the probability that chamber B is empty, and specifically how does this compare to the chance of chamber A being empty (w...
by Cauchy
Sun Feb 07, 2016 12:42 pm UTC
Forum: Mathematics
Topic: Coin flip problem
Replies: 6
Views: 1921

Re: Coin flip problem

This is a trick I learned once for the "drunkard's walk" formulation. Let X k equal the number of heads minus the number of tails after k tosses. The probability that X k stays below m forever is equal to P(X n < m) - P(X n < m and X k = m for some k). For each sequence of flips in the la...
by Cauchy
Sat Feb 06, 2016 12:03 pm UTC
Forum: Logic Puzzles
Topic: Six roll dice game
Replies: 11
Views: 3732

Re: Six roll dice game

I think Jeff's answer makes sense. The rolls are independent so it doesn't matter if you rolled 0 times or 5 times before. The fact of the matter is you have a total of six trials to get a desirable value. The probability of there being at least one 6 is: P 6 = 1-(5/6)^6 = ~0.6651 The p...
by Cauchy
Sat Feb 06, 2016 11:37 am UTC
Forum: Mathematics
Topic: Well-ordered Subset of Reals
Replies: 8
Views: 3217

Re: Well-ordered Subset of Reals

For limit ordinals, shrink all of the predecessors, then put them on (0,1), (1,2), etc.; there's countable many (and they're countable, so by definition we have a bijection from them to the naturals, no choice worries), so we can do this. This argument doesn't work, because the bijection must prese...
by Cauchy
Thu Feb 04, 2016 8:44 am UTC
Forum: Mathematics
Topic: Infinite balls
Replies: 6
Views: 2612

Re: Infinite balls

This kind of thing shows up in analysis all the time, and the question in the opening is just a discrete version of that. In analysis, the only sensible candidate for a limit of functions is the pointwise limit, that is if f is the limit of f_1, f_2, etc., then it must be the case that f(x) is the l...

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