Search found 52 matches

by campboy
Tue Apr 26, 2016 3:55 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1672: "Women on 20s"
Replies: 218
Views: 39763

Re: 1672: "Women on 20s"

Does that 1/5 figure include her majesty? No. And arguably that figure is misleading anyway since there are only four banknotes. (It's only 1/5 because two men share the £50.) The current controversy in the UK is not principally about the ratio, though. The issue is that the next two scheduled chan...
by campboy
Fri Jan 31, 2014 3:35 pm UTC
Forum: Mathematics
Topic: (homework) x^3-9 mod 31 irreducible.
Replies: 6
Views: 2653

Re: (homework) x^3-9 mod 31 irreducible.

True. I meant that you don't need to know the multiplicative group of F_p is cyclic.
by campboy
Thu Jan 30, 2014 11:05 am UTC
Forum: Mathematics
Topic: (homework) x^3-9 mod 31 irreducible.
Replies: 6
Views: 2653

Re: (homework) x^3-9 mod 31 irreducible.

In this particular case, all you need is Fermat's Little Theorem.
by campboy
Mon Jan 06, 2014 11:08 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1313: "Regex Golf"
Replies: 64
Views: 27440

Re: 1313: "Regex Golf"

Also, a number of presidents have been in office without ever being elected as president; does the regex match them or not? Nine people have been president without previously being elected as president. Of those, five were subsequently re-elected, and another has the same surname as one of the five...
by campboy
Tue Sep 10, 2013 10:12 am UTC
Forum: Logic Puzzles
Topic: Towers, Courtyard, and trees
Replies: 36
Views: 13849

Re: Towers, Courtyard, and trees

I used to think that the above solution was the correct one for this riddle. A friend of mine disagrees, and I'm not so sure any more. I post his solution here. Can someone spot any problems with it? My (somewhat informal) reaction to it is that it assumes that certain facts are common knowledge, w...
by campboy
Mon Sep 02, 2013 9:43 am UTC
Forum: Mathematics
Topic: The Tau Manifesto
Replies: 165
Views: 44049

Re: The Tau Manifesto

IMO the tau campaign goes wrong right at the start. If you are going to write the circumference of a circle in terms of something, the diameter is the right choice. The relationship [imath]C=\pi d[/imath] generalises to Barbier's theorem, that any curve of constant diameter [imath]d[/imath] has perimeter [imath]\pi d[/imath].
by campboy
Wed Aug 28, 2013 10:11 am UTC
Forum: Mathematics
Topic: Throwing a random die
Replies: 20
Views: 5076

Re: Throwing a random die

I believe it's known that the probability of a cuboctahedron (say) landing on a square face varies as you throw it onto different surfaces. I went to a recreational maths talk by Frank Berkshire many years ago where he gave a model which came up with plausible results, but couldn't find any details ...
by campboy
Wed Jan 09, 2013 7:14 pm UTC
Forum: Logic Puzzles
Topic: Solve ALL of the Mazes [solutions]
Replies: 29
Views: 9038

Re: Solve ALL of the Mazes [solutions]

4. If all 4 directions are needed, still working on a proof. Well, the necessary steps could be up, left, left, down, down, down, right, right, which doesn't always keep you at the exit. There was an assumption that the exit is always in the lower right and the start is always in the upper left. So...
by campboy
Wed Jan 09, 2013 6:56 pm UTC
Forum: Logic Puzzles
Topic: Solve ALL of the Mazes [solutions]
Replies: 29
Views: 9038

Re: Solve ALL of the Mazes [solutions]

4. If all 4 directions are needed, still working on a proof. Well, the necessary steps could be up, left, left, down, down, down, right, right, which doesn't always keep you at the exit. You can, however, always do any two mazes A, B simultaneously. Suppose you start with a solution to A, and then ...
by campboy
Thu Sep 20, 2012 8:00 am UTC
Forum: Mathematics
Topic: The uses of log10
Replies: 17
Views: 4052

Re: The uses of log10

For me the question is "why isn't there a log2x button?"
by campboy
Sat Jul 28, 2012 11:10 am UTC
Forum: Logic Puzzles
Topic: Price Is Right
Replies: 8
Views: 3344

Re: Price Is Right

Perhaps surprisingly, they should all end up with an equal chance of winning, by guessing (in order) $2251, $1501, $751, $1. With the first three as above, fourth player does worse by choosing anything other than $1. If the first two are the same then any play by third of more than $751 does...
by campboy
Wed Jul 04, 2012 10:26 am UTC
Forum: Logic Puzzles
Topic: 999,999 sticks
Replies: 7
Views: 4357

Re: 999,999 sticks

In fact you can never do it if n+1 is not square: Combining lorb's bound with what jaap did, we need to find k with 1<k\leq \sqrt{n+1} such that \frac{n(n+1)}{2} is a multiple of n+1-k. Equivalently, we need \gcd\big(n+1-k,\frac{n(n+1)}{2}\big) to equal n+1-k. But \gcd\bi...
by campboy
Fri Jun 22, 2012 5:22 pm UTC
Forum: Mathematics
Topic: Making the most out of a djinn's offer
Replies: 14
Views: 3317

Re: Making the most out of a djinn's offer

The game suggested in the OP is a variation on the http://en.wikipedia.org/wiki/St_Petersburg_Paradox . It should be easy enough to come up with a figure which is enough for all practical purposes, provided the djinn isnt going around making the same offer to other people and thereby devaluing the c...
by campboy
Thu Mar 22, 2012 9:24 am UTC
Forum: Mathematics
Topic: Exponential versus factorial
Replies: 3
Views: 2779

Re: Exponential versus factorial

Stirling's formula is much more powerful than you need for this. It's sufficient to use the inequalities \left(\frac{n}{e}\right)^n < n! < ne\left(\frac{n}{e}\right)^n for n at least 2, which are easy to prove by induction using the fact that \left(1-\frac{1}{n}\right)^n < \f...
by campboy
Wed Jan 04, 2012 2:26 pm UTC
Forum: Logic Puzzles
Topic: The motorbike and the car.
Replies: 24
Views: 6635

Re: The motorbike and the car.

I think the simplest way of looking at it is as follows. In the time taken for the motorbike to accelerate to 60km/h, the car goes 6m further than the motorbike. The average speed of the bike over that period is 30km/h and so the car is 30km/h faster on average, so will travel 6m further than the bi...
by campboy
Wed Jan 04, 2012 12:46 pm UTC
Forum: Logic Puzzles
Topic: The Mysterious Coin
Replies: 34
Views: 12129

Re: The Mysterious Coin

I have a problem, assuming uniform prior you flip the coin and it comes up heads three times and tails once, what is the probability that on the next toss it will come up heads? If you flip a+b times and get a heads and b tails the probability of a head on the next go is \frac{\int_0^1p^{a+1}(1...
by campboy
Sat Aug 13, 2011 10:16 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0936: "Password Strength"
Replies: 893
Views: 317222

Re: 0936: "Password Strength"

Of course these circumstances might not obtain, but my point is that "how hard is it to search the set of passwords matching this pattern?" is not the only important question; "how often are passwords matching this pattern used?" is just as important. One is the cost and one is ...
by campboy
Fri Aug 12, 2011 8:24 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0936: "Password Strength"
Replies: 893
Views: 317222

Re: 0936: "Password Strength"

Maybe I'm missing something, but it seems that everyone here is discussing the strength of passwords of a given pattern, against an attacker who knows to try that pattern ; yet as this thread shows, people have many different patterns they use. Each of them has a varying strength against an attacke...
by campboy
Fri Nov 19, 2010 6:30 pm UTC
Forum: Mathematics
Topic: What does it mean for a set to be "Ramsey"
Replies: 3
Views: 780

Re: What does it mean for a set to be "Ramsey"

A finite set X in Rd is Ramsey if for any k there exists n such that any k-colouring of Rn contains a monochromatic copy of X.
by campboy
Thu Jul 29, 2010 11:23 pm UTC
Forum: Logic Puzzles
Topic: Cat and mouse
Replies: 29
Views: 13776

Re: Cat and mouse

post deleted
by campboy
Fri Jun 25, 2010 12:49 pm UTC
Forum: Logic Puzzles
Topic: Minimum Number of Orderings
Replies: 3
Views: 1352

Re: Minimum Number of Orderings

Well, here's an upper bound: we can find such a set of size n. Proof: We claim that in fact there exists such a set of size n with the additional property that there is one permutation starting with each element. We prove this by induction; S(3)={123, 312, 231} is such a set for n=3. Suppose...
by campboy
Thu Jun 10, 2010 11:33 am UTC
Forum: Mathematics
Topic: "Special" four digit number
Replies: 26
Views: 8707

Re: "Special" four digit number

meatyochre wrote:I like 3927, simply because it's 3^1, 3^2, 3^3.

It's also my pin number for pretty much everything. But I don't worry about admitting that :P


Also, 39 books in the Old Testament and 27 in the New (not including the Apocrypa).
by campboy
Thu Jun 10, 2010 10:35 am UTC
Forum: Logic Puzzles
Topic: Rotating Doubles Teams
Replies: 1
Views: 1060

Re: Rotating Doubles Teams

You should be able to adapt Howell bridge movements to do essentially what you want. Try googling for that.
by campboy
Sun May 23, 2010 12:52 pm UTC
Forum: Logic Puzzles
Topic: A number game
Replies: 21
Views: 8453

Re: A number game

jestingrabbit wrote:Picking a high number does decrease your chance of draw. I was assuming that counted as a do over.

Ah, ok, I was assuming you only play the game once, and are trying to maximise your win chance. Which shows that I didn't read the link carefully enough :oops:
by campboy
Sun May 23, 2010 10:11 am UTC
Forum: Logic Puzzles
Topic: A number game
Replies: 21
Views: 8453

Re: A number game

I knew this had come up before. http://forums.xkcd.com/viewtopic.php?f=3&t=3171 And here's a link that's given there to a solution for the case n=3. http://www.greylabyrinth.com/puzzle/206 That solution is not correct. If both other players play that strategy, and you pick 1, you win if and onl...
by campboy
Sat May 22, 2010 3:51 pm UTC
Forum: Logic Puzzles
Topic: Not as easy as 1 2 3
Replies: 56
Views: 14245

Re: Not as easy as 1 2 3

Token wrote:
campboy wrote:
Spoiler:
If you're allowed to add together that many odd primes, can you get every sufficiently large integer of the appropriate parity?

Spoiler:
Aren't both 2 and 3 "don't know"s?

by campboy
Fri May 21, 2010 8:54 pm UTC
Forum: Logic Puzzles
Topic: Not as easy as 1 2 3
Replies: 56
Views: 14245

Re: Not as easy as 1 2 3

Spoiler:
If you're allowed to add together that many odd primes, can you get every sufficiently large integer of the appropriate parity?
by campboy
Fri May 21, 2010 8:30 pm UTC
Forum: Logic Puzzles
Topic: Pairing Problem
Replies: 11
Views: 2472

Re: Pairing Problem

I don't understand why this is a problem, assuming you have a computer. Start with the numbers 0 up to 51 (0 is the bye). Pick two unmatched numbers at random and match them. Repeat until you have 26 matched pairs. Now run through the pairs and check each one against your list of forbidden pairs (pa...
by campboy
Fri May 21, 2010 8:20 pm UTC
Forum: Logic Puzzles
Topic: A number game
Replies: 21
Views: 8453

Re: A number game

Suppose we are playing with n players, and have a strategy S in which there is a largest number chosen with non-zero probability, k, say. If n-1 of the players are known to be using strategy S then the final player wins more often if he plays strategy S' than he does if he plays strategy S, whe...
by campboy
Wed Feb 10, 2010 12:56 pm UTC
Forum: Logic Puzzles
Topic: birdwatchers
Replies: 14
Views: 3464

Re: birdwatchers

Sorry, missed Gopher's post (it was short :)). Anyway, a lot of the discussion above is answering a completely different problem, so it is no surprise that a different scheme is best. The original problem asked us to maximise the probability of everyone getting called, not to maximise the expected n...
by campboy
Tue Feb 09, 2010 2:26 am UTC
Forum: Logic Puzzles
Topic: The Bobs
Replies: 37
Views: 5012

Re: The Bobs

Now the solution: Cesar Cipher, Shifted 3 characters WKHUH LV RQOB RQH ERE, ZLWK PXOWLSOH SHUVRQDOLWLHV DOO RI ZKLFK DUH QDPHG ERE DQG ZHUH "FRQFHLYHG" DW GLIIHUHQW WLPHV, DQG DUH RI GLIIHUHQW DJHV. In what sense is that a "solution"? The question asked for Bob's age (and Bob's,...
by campboy
Mon Feb 08, 2010 12:35 pm UTC
Forum: Logic Puzzles
Topic: birdwatchers
Replies: 14
Views: 3464

Re: birdwatchers

Heuristically, the following seems right if the probability p of a twitcher failing to call is small (and the right asymptotic to consider is probably a scheme where p=O(1/N)). Each person is supposed to call two others, so on average each person is called by two others. If someone is called by more...
by campboy
Mon Dec 14, 2009 3:16 pm UTC
Forum: Logic Puzzles
Topic: Optimal strategy for Double Bullseye and variants
Replies: 4
Views: 1461

Re: Optimal strategy for Double Bullseye and variants

Suppose there are n possible prices left, x to x+n-1. I claim that if n is even, then you have a 1/2 probability of winning if you make any valid guess, assuming perfect play thereafter, whereas if n is odd then your correct strategy is to pick x+2k for any k, after which with perfect play by both ...
by campboy
Mon Dec 14, 2009 2:27 pm UTC
Forum: Logic Puzzles
Topic: Eli the Slacker
Replies: 10
Views: 2005

Re: Eli the Slacker

however, because of security reasons, the exam is printed in several versions, where the questions and answers are exactly the same, but in different order, so that the answer patterns are different... Ah, it seems I misunderstood this first time round. I thought it meant the questions were reorder...
by campboy
Sun Dec 13, 2009 8:42 pm UTC
Forum: Logic Puzzles
Topic: Eli the Slacker
Replies: 10
Views: 2005

Re: Eli the Slacker

With this sort of problem it is probably right to think of v as a function of N rather than constant, in order to get something interesting. Are we intended to regard the answer key itself as random? If it is fixed (and the permutations used for the different versions are also fixed) it is certainly...
by campboy
Thu Dec 10, 2009 7:27 pm UTC
Forum: Logic Puzzles
Topic: The expanding bar
Replies: 19
Views: 4047

Re: The expanding bar

Slightly different approach: Putting lengths in miles, fix the ends 20 apart, with the bar being an arc with height h, and let the radius of the circle be r, with the angle between radii from the middle of the bar and from one end being \theta . Then 10=r.sin\theta . Also, by intersecting chords, 10...
by campboy
Sun Dec 06, 2009 4:09 pm UTC
Forum: Logic Puzzles
Topic: Mastermind
Replies: 19
Views: 3799

Re: Mastermind

aabc - with b/w = 0/1, has 1123 possible outcomes (though it's 2nd and 3rd highest are lower than aabb's) How on earth do you get that figure? It must be wrong, surely, as that would mean 86% of the possible codes get a score of 0/1. I get that for aabc the codes divide up as follows, though I may ...
by campboy
Thu Dec 03, 2009 12:53 am UTC
Forum: Logic Puzzles
Topic: Mastermind
Replies: 19
Views: 3799

Re: Mastermind

My understanding from reading the wikipedia article was that the total number of pegs awarded for green, say, is the smaller of (number of greens in code), (number of greens in guess). Is this right? In particular it would mean that the marking scheme is symmetric, and that you get a total of 4 pegs...
by campboy
Mon Nov 23, 2009 9:13 pm UTC
Forum: Logic Puzzles
Topic: Five triangles
Replies: 6
Views: 2005

Re: Five triangles

He says "subdivide"; in other words we need the small triangles to cover the main triangle, to not overlap (except on their boundaries) and to not extend outside the main triangle.
by campboy
Thu Oct 08, 2009 4:01 pm UTC
Forum: Logic Puzzles
Topic: Question on probability
Replies: 8
Views: 1798

Re: Question on probability

Yes, to put it another way
Spoiler:
the number of successes from n trials with probability a/n tends to a Poisson distribution with parameter a
.

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