## Search found 52 matches

Tue Apr 26, 2016 3:55 pm UTC
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...
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.
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.
Mon Jan 06, 2014 11:08 am UTC
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...
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...
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].
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 ...
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...
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 ...
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?"
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...
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...
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...
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...
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...
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...
Sat Aug 13, 2011 10:16 am UTC
Replies: 893
Views: 317222

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 ...
Fri Aug 12, 2011 8:24 am UTC
Replies: 893
Views: 317222

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...
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.
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
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...
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

Also, 39 books in the Old Testament and 27 in the New (not including the Apocrypa).
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.
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
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...
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?

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?
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...
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...
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...
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,...
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...
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 ...
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...
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...
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...
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 ...
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...
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.
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
.