Search found 30 matches

by gcoope
Wed Jun 01, 2011 1:33 am UTC
Forum: Logic Puzzles
Topic: Which coin?
Replies: 10
Views: 3488

Re: Which coin?

Spoiler:
Flip the bent coin into his water?
by gcoope
Tue Apr 26, 2011 11:02 pm UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

Looks correct to me, very interesting indeed. As an intuition I'd say the 1/n strategy is probably best for large n, but would love to hear an improved bound, particularly if it came with a better strategy.
by gcoope
Tue Apr 26, 2011 11:00 pm UTC
Forum: Logic Puzzles
Topic: How many prisoners?
Replies: 112
Views: 46321

Re: How many prisoners?

This is not at all the case. Suppose the first night, the sequence goes YOU, A, B, such that B will see A's message, and A will see yours. So we have: YOU, A, B; A gets the bit YOU, A, B; B gets the bit _,YOU,B,A; A gets the bit _,_,YOU,A,B; B gets the bit ... In the answer I gave the prisoners kee...
by gcoope
Mon Apr 25, 2011 11:57 pm UTC
Forum: Logic Puzzles
Topic: How many prisoners?
Replies: 112
Views: 46321

Re: How many prisoners?

Not so, the warden can control the path of the message through the prisoners. They could loop it back to you in any amount of time they choose including as many or few of the prisoners as they chose. I believe as stated the problem is equivalent to the warden re-wiring the switches however they wis...
by gcoope
Mon Apr 25, 2011 10:54 pm UTC
Forum: Logic Puzzles
Topic: How many prisoners?
Replies: 112
Views: 46321

Re: How many prisoners?

The prisoners can find an upper limit on their population: At first only prisoner 1 (that's me) is an Alpha, the rest are Betas. The prisoners alternate between "spreading" and "zeroing". The "spreading" round lasts only one night, in it anyone who is an Alp...
by gcoope
Mon Apr 25, 2011 4:39 pm UTC
Forum: Logic Puzzles
Topic: How many prisoners?
Replies: 112
Views: 46321

Re: How many prisoners?

What does the 1/10th of a second limit mean for the prisoners? Can they react in this time and turn their switch? Or do they just find out whether the switch in the room next to them is on or off? Even if they cannot react in this time, can they switch the switch over in this 1/10th of a second? Do ...
by gcoope
Fri Apr 22, 2011 11:26 am UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

That doesn't quite fit what I intended to say: When I said that the prisoners only ever leave the switch on, I meant that none of them ever leave it off. Not even finitely many times. Not even once. So you are breaking it down as If 50 prisoners are sent in a room with a lightswitch that is off...
by gcoope
Thu Apr 21, 2011 3:49 pm UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

Don't quite have my head around the second part yet. My tiny contribution to the question is an improved strategy for the prisoners when n=4. Instead of the strategy suggested by sfwc, the prisoners do this: If on their first trip they see the switch off, they give up their soul and become a non-cou...
by gcoope
Mon Apr 18, 2011 11:06 pm UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

@krucifi. In that case I'm afraid I really don't understand your idea or what a cycle is. You asked to be told if your line of reasoning is bogus and I can tell you that it is. It's been shown earlier in the thread that there is no winning strategy for the prisoners. If you think you hav...
by gcoope
Mon Apr 18, 2011 10:27 pm UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

@ Yakk. Yes this was a key component to my argument earlier as to why the warden always wins, I just explained it fairly horribly. @ krucifi. You seem to be making two major mistakes as far as I can make out. Firstly you are allowing the prisoners a way of distinguishing themselves, so that differen...
by gcoope
Thu Apr 14, 2011 8:08 am UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

@ WarDaft It appears you are now looking at the question of whether you can give the prisoners a chance of escaping with a non-deterministic algorithm, and trying to reduce the probability of this by increasing the expected number of visits that must be made. However it doesn't quite work like that....
by gcoope
Wed Apr 13, 2011 12:57 am UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

Second, although gcoope's argument works for 100 prisoners, his extension to odd numbers of prisoners doesn't quite work: The prisoners apart from the one you singled out at the start might end up always returning 0s, and then you couldn't ever reintroduce the original prisoner without enda...
by gcoope
Tue Apr 12, 2011 12:50 am UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

Sorry, I understood the first position they see to also be their first sequence they are looking for. If you want a and c to see another 0 and b and d to see another 1 just try:

a, b, a, b, c, d, c, d

now they will all just leave it on 0.
by gcoope
Tue Apr 12, 2011 12:07 am UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

Woops, I let the warden make a slight error, that might be important... Also, my solution involves more communication between the prisoners than is immediately apparently possible, so it should avoid at least the basic pitfalls. You can follow my argument with your strategy fairly well, hopefully i...
by gcoope
Mon Apr 11, 2011 11:51 pm UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

I think I have this solved for any reasonably simple strategies, see my earlier post, I know it's not written out hugely clearly.

@Ansain...how do your prisoners choose between their two options? Even though they know the warden is malicious I don't see how this helps.
by gcoope
Mon Apr 11, 2011 9:05 pm UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

Never mind, found an obvious failure pattern for my strategy while trying to write up an explanation of it. Feel free to read it for ideas, but it doesn't actually work. Hmm, further thinking I don't have time to fully expand and analyze atm: what if every prisoner had a direction of count as part ...
by gcoope
Mon Apr 11, 2011 8:02 pm UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

Yakk, thanks for the in-depth look at my idea. I have updated my post to try and clarify the Lemma, although I think you got it. You are right that the warden must be able to determine the long term behaviour of a single prisoner if they are repeatedly put in the room, which is a bigger question tha...
by gcoope
Mon Apr 11, 2011 6:22 pm UTC
Forum: Logic Puzzles
Topic: A twist on the switch problem
Replies: 57
Views: 10613

Re: A twist on the switch problem

I think I have a solution to this, mega post incoming, would definitely like someone to check it! The warden can always screw the prisoners. The strategy is deterministic, and the same for all the prisoners. Furthermore each prisoners strategy on each go is uniquely determined by the state of the sw...
by gcoope
Mon Nov 22, 2010 5:35 pm UTC
Forum: Logic Puzzles
Topic: 20 prisoners
Replies: 29
Views: 8439

Re: 20 prisoners

Do the two switches share the same type of "states"?
by gcoope
Thu Sep 10, 2009 10:00 am UTC
Forum: Logic Puzzles
Topic: Ordering of Vases [solution]
Replies: 25
Views: 4886

Re: Ordering of Vases [solution]

jaap wrote:
gcoope wrote:Sorry, I could've been clearer. The start of the permutation is a permutation of all the odd numbers.

For N = 10

(1,3,5,7,9),(2,6,10),4,8

where you can permute the numbers in brackets


But you cannot have 7 between 5 and 9, 6 between 2 and 10, etc.

Oops!
by gcoope
Thu Sep 10, 2009 9:35 am UTC
Forum: Logic Puzzles
Topic: Ordering of Vases [solution]
Replies: 25
Views: 4886

Re: Ordering of Vases [solution]

How about just arrange the numbers thus, 1 mod 2, 2 mod 4, 4 mod 8 ..... This (and its reverse) give a large proportion of the permutations I believe. I have no idea what you mean by this. 1 mod 2 = 1 2 mod 4 = 2 4 mod 8 = 4 So your sequence goes 1, 2, 4, ... then what? Sorry, I could've been clear...
by gcoope
Thu Sep 10, 2009 9:22 am UTC
Forum: Logic Puzzles
Topic: Ordering of Vases [solution]
Replies: 25
Views: 4886

Re: Ordering of Vases [solution]

to find a suitable arrangement of N vases, we take n with 2 n >N, take the permutation f n (id 0 ) which defines a suitable arrangement of 2 n vases, and omit vases N,...,2 n -1 , and probably add 1 to each number , so the vases are numbered 1 to N rather than 0 to N-1. This algorithm gives you a l...
by gcoope
Thu Sep 10, 2009 8:08 am UTC
Forum: Logic Puzzles
Topic: Ordering of Vases [solution]
Replies: 25
Views: 4886

Re: Ordering of Vases [solution]

Except its unlikely there is a vase of height 0 and if N isn't a power of two then you won't have a permutation.


How about just arrange the numbers thus,

1 mod 2, 2 mod 4, 4 mod 8 .....

This (and its reverse) give a large proportion of the permutations I believe.
by gcoope
Tue Jul 21, 2009 7:48 am UTC
Forum: Logic Puzzles
Topic: Infinite queens on an infinite chessboard
Replies: 35
Views: 26250

Re: Infinite queens on an infinite chessboard

That's not quite right userxp, you can't guarantee that you will ever get to a specified row/column/diagonal. However with a little twerk: There are a countably finite total number of rows/columns/diagonals. Therefore we can give them an index with the natural numbers. For the lowest index line whic...
by gcoope
Tue Jul 07, 2009 2:49 pm UTC
Forum: Logic Puzzles
Topic: A selection of puzzles...
Replies: 29
Views: 3626

Re: A selection of puzzles...

#8
Spoiler:
The track straight after these words is "Eple".

"Eple" is Norwegian for "Apple".

So the answer is "apple" or "iPhone" maybe?
by gcoope
Fri Jun 19, 2009 7:13 pm UTC
Forum: Logic Puzzles
Topic: Complete the sequence!
Replies: 8
Views: 2072

Re: Complete the sequence!

Ew, googled it, it isn't really a logic puzzle, specific prior knowledge definitely required.

More numbers isn't going to help you.
by gcoope
Wed May 20, 2009 10:29 pm UTC
Forum: Logic Puzzles
Topic: tangent circles
Replies: 26
Views: 3761

Re: tangent circles

I'm fairly confident that you can get more than four in 3-space with the definition "touching at exactly one point" (which is a reasonable enough definition, considering any plane containing the linear direction at the adjacency point could be considered "parallel") I don't thin...
by gcoope
Tue May 19, 2009 9:58 pm UTC
Forum: Logic Puzzles
Topic: tangent circles
Replies: 26
Views: 3761

Re: tangent circles

Surely in 3-dimensions "tangent" could still mean that the two circles meet at a point and the tangent line is shared, rather than a plane... It seems a far more "reasonable" meaning of the word "tangent" to me....still can't get more than 4 though. I suspect a better 3...
by gcoope
Sun May 17, 2009 12:44 pm UTC
Forum: Logic Puzzles
Topic: A real function taking every value on every interval
Replies: 8
Views: 2768

Re: A real function taking every value on every interval

Yeah, I was trying to do something like that with the continued fraction expansion. Let n = the number of 1's in the continued fraction expansion, k= the number of 2's and a = the asymptotic density of 3 in the representation. If n or k is infinite, let f(n) = 0, else let f(x...
by gcoope
Sun May 17, 2009 12:02 pm UTC
Forum: Logic Puzzles
Topic: A real function taking every value on every interval
Replies: 8
Views: 2768

Re: A real function taking every value on every interval

Here's a constructive one which doesn't require the axiom of choice. Consider the ternary expansion of the fractional part of each number, x. Now if x has has infinite number of 2s in its expansion f(x)=0. If x has a final 2 in it's expansion then f(x) is in binary the digits whi...

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