UKC

http://www.bbc.co.uk/news/world-asia-32297367

No wonder Singapore succeeds

http://www.ukmt.org.uk/b_file.php?id=788

In reply to m0unt41n:

Perhaps you would like to see the uk version.

Examples above.

In reply to marsbar:
All right, it is obvious why May 19th and June 18th can be eliminated - Bernard would know as these are unique numbers. But the worked example seems to say that all May dates and all June dates are also eliminated by that test, the further reasoning depends on this point. Why should this be, when the only information is that the number date alone cannot be sufficient to identify the answer?

In reply to Simon4:
Remember that Albert already knows the month. It's because he knows it isn't May or June that he knows Bernard can't tell which date it is from the number alone.

In reply to deepsoup:
But how does that eliminate say May 15th from August 15th? Is there enough evidence in the question to conclude this? All statement 1 tells you is that it is not a unique number, so the number is not enough to tell Bernard when it is.

Albert knows the month. But how can you, using only the evidence given in the question (you do NOT know what Albert knows), conclude that it is July 16th rather than May 16th?

I suppose what I mean is how can Bernard, using the knowledge that Albert does not know the date but DOES know that he also does not know it, can conclude that it is NOT May 16th. He knows it is a 16th, but how can he eliminate one of them, on the basis that Albert does not know and knows that he does not know?

In reply to Simon4:
We know that
Albert has only been told the month
Albert knows that Bernard has only been told the day
Albert has deduced that Bernard can't possibly know the date exactly.

if it was possible that it was May 19th, then Bernard could possibly know the date exactly
hence Albert must have evidence that it can't be May 19th
the only way that Albert can have evidence that it isn't May 19th is if he's been told that it's a month other than May.

The other stages are pretty similar.

In reply to Simon4:


The same way we know.

Albert knows that Bernard knows the number. There is only one 18 and only one 19, so for Albert to be sure that Bernard doesn't know the date he must know that it isn't May 19 or June 18.

Albert doesn't know the number, but he does know the month. So the only way he can be sure that it isn't May 19 or June 18 is if he knows that it isn't May or June.

So as soon as he says he knows that Bernard doesn't know, we (and Bernard) can work out that it isn't May or June.

Bernard already knows the number. So as soon as he finds out that it's either July or August, he knows the whole date. (Albert still knows only which month.)

When Bernard says that he knows the whole date, Albert knows that it can't be the 14th - because then Bernard would still not have known whether it was July 14th or August 14th.

Albert already knows the month so knowing it can't be the 14th, he knows the whole date too.

When Albert says that he knows the whole date, that tells us that it has to be in July. Because if it were August, Albert still wouldn't know whether it was August 15 or August 16.

So now we know it's July, and we found out earlier that it couldn't be the 14th so it has to be July 16th.

I think it's slightly less confusing if you think of it as a problem with three people in it. Albert, Bernard and Charlie. (Charlie is us.)

When Albert says he knows Bernard doesn't know, Bernard can work out the date.
When Bernard says he's worked it out, Albert can work it out too.
When Albert says he's worked it out, Charlie can finally work it out as well.

In reply to m0unt41n:

So far so groovy... But from the picture given, what i really want to know is whether the problem was white and gold or blue and black?

In reply to Simon4:

You have really good explanations, are you happy about the logic now?

I think all these problems are variations on the black-and-white-hats-convicts-in-a-line type(*).

Implicit is the idea that the folk in the problem are good at solving logic problems.

* Bjartur i Sumarhus post:
http://www.ukclimbing.com/forums/t.php?t=612631&v=1#x8019175
Four prisoners are buried up to their necks in the ground. Three in a row , one behind the other, all facing the same direction (so only one at the back can see the other two, and the middle guy can only see the one in front, and the front guy can't see anyone), and one on the otherside of a brick wall (so out of sight of the other three, but they know he is there). All fo them are wearing a hat. There are two white hats and two black hats, and the prisoners know this.

The guard decides to play an evil game and tells them that one of them has to tell him which colour hat they are wearing, or he will shoot them all. They cannot guess, and he gives them 5 seconds for one of them to decide.

My bit:
They are positioned like this:

B | B W B

In reply to marsbar:

Indeed, the problem didn't seem more difficult than ones that get asked in similar tests here.

In reply to lowersharpnose:

"My bit: They are positioned like this: B | B W B"

Shouldn't that be W | B W B

In reply to Bjartur i Sumarhus:
There isn't enough information to work out how they're positioned is there? Or which prisoner will figure it out. Only that (if they're really smart) either one of them will get it straight away, or another will realise that one doesn't know and get it a few seconds afterwards. If the first guy gets it he'll know where all four are, if the second guy gets it he'll only know his own and the guy in front.

Edit to add:
Real world answer: they're going to get shot. Just a matter of time. The guard has made up his mind that he's going to shoot them all and is just having a bit of twisted fun first.

It's like the Garden of Eden. All that business with the apple - there's no way the sort of god who'd set a trap like that was just going to say "ah well, fair enough" and leave them in peace if they hadn't fallen for it. There'd have been another test, and another - as many as necessary, but Adam and Eve were always going to get kicked out regardless. Nothing they could do about it, that's just the sort of supreme being they were dealing with. What an omniscient, omnipotent, all wise, infinitely compassionate bell-end!

In reply to deepsoup:

There is enough info as explained in the other thread that LSN has referenced.

Using the example B | W W B (where letter denotes colour of hat worn in oder of buried prisoners) then the chap at the back of the line (on the right) can see two white hats, therefore he knows he must be wearing black and would shout out immediately.

If the order is B | W B W then the chap at the back cannot tell without guessing as he can see a white and a black hat. In this senario, the chap in front of him can conclude correctly that he must be wearing a different colour to the guy in front of him (nxt to the wall) if there is no answer from behind him, so he can shout out "Black" and save them.

In reply to Bjartur i Sumarhus:

I think you have the puzzle wrong. With 2 white and 2 black it's trivial for the end or middle person to get the answer.

In the original puzzle there are 3 white and 2 black. It's a little harder.

In reply to Bjartur i Sumarhus:

Looking up the 5 hat version, I found an even better puzzle.

3 people are in a room, they can only see the other 2 hats. The hats are red or blue and randomly assigned (so each can be either). They simultaneously have to guess their hat colour (or pass) and if their are only correct answers (excluding passes) they will all 3 share a prize. If any of them answers incorrectly they all lose. If they all "pass" they get nothing.

They can discuss a strategy before the hats are assigned but no communication/signal can be used.

There is no 100 % solution, and if one is defined as the guesser and they just choose to go with Red they will have a 50% chance. What method provides a better than 50% chance?

In reply to m0unt41n:

I thought I'd got it, then looked at the solution and realised why I was wrong. That is a clever little puzzle, and quite hard.

In reply to Bjartur i Sumarhus:

Oh, right. Ta. I was just looking at this thread.