Recent posts by beauval on Kongregate

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Topic: Serious Discussion / Logic Puzzle

Yes, you’re right, I didn’t take that to its logical conclusion. I remembered broadly how the solution was worked out, but it still took quite a long time to get that far. It was getting very late, and I couldn’t be bothered to do any more checking. Mind you, in pirate A’s position I would have seen 95 percent as a pretty decent result.

 
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Topic: Serious Discussion / Logic Puzzle

If the first three pirates get it wrong, we are left with the two youngest. Calling them A,B,C,D,E, with D & E left, D has to give all the loot to E. Otherwise E will vote against the plan and D goes over the side.

With three pirates left, E will vote against any plan because he knows that if he gets rid of C, he will be on to a winner. D, on the other hand, knows he is sure to die in that situation, so will accept just 1% of the loot to avoid that. So C divides the loot 99/1 with D, and E gets nothing.

Moving on to 4 pirates (and this is the tricky one), B needs the support of 2 other pirates, otherwise he becomes shark bait. So he gives 2% to D and 1% to E, which makes them better off to vote for B’s plan. In that scenarion C gets nothing.

So with 5 pirates, A needs to get 2 votes plus his own. So he gives D 3% and E 2%, keeping 95% for himself.

 
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Topic: Serious Discussion / Logic Puzzle

I think that is probably crucial.

 
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Topic: Serious Discussion / Logic Puzzle

I’ve seen this before, and it goes something like this. I can’t remember if this is the complete solution, but I can’t see any holes in it yet.

The oldest pirate gives 1% each to the two youngest to get their votes. They accept what on the face of it is a crappy deal because if they don’t the oldest pirate will be slung overboard, leaving four. The two next oldest pirates would then share the loot and vote to keep it, leaving the two youngest with nothing at all.

 
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Topic: Serious Discussion / The next President Clinton

Setting aside the asinine inference that the right hates female leaders

When the news broke, I had a look at a range of opinion pieces and blogs. Being a woman did seem to be an issue on some of them. I know you can write them off as just blogs, but it’s idiots with big mouths who elect leaders just as much as any other group.

Well, for that we would want to look at her policies and record, and that’s apparently off limits. I think that’s the better question, frankly.

Not entirely off limits, but I didn’t want this to become another Reps v Dems arguement. Maybe what I saw was unrepresentative, but I got the feeling that being a woman is going to be a big disadvantage to her. There have been women in high places before – Madeleine Albright, Condoleza Rice etc. – but they weren’t voted into those positions by the public. Hillary needs public support, and I’m wondering to what extent being a woman will affect her chances.

We’ve been through this before over here, but we do things a bit differently over here. Maggie Thatcher was already leader of the Conservative party when she went into her first general election. She was in a pretty safe constituency, so it was a foregone conclusion that she would become PM if she won. But the issue of being a woman came up over and over. It was still quite a revolutionary idea back then, and was used against her by her political enemies.

So I think the question is relevant.

 
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Topic: Serious Discussion / The next President Clinton

So it’s now official – Hillary Cinton is having another crack at the American presidency. Now then, a simple question. Is a country as deeply conservative as America ready for a woman in the White house, especially one who is (by American standards) a left winger?

I’m not interested in the rights and wrongs of her policies at this point – just stick to the question.

 
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Topic: Serious Discussion / Full Body Transplants a Reality on a Personal Level

I can remember when Christiaan Barnard performed the first heart transplant. The early patients didn’t last long, but in a way that didn’t seem to matter. It was the mere fact that it had been done that was so sensational. We knew that the medical teams would learn from their mistakes, and the process would get better.

So I expect similar results if this surgery does actally take place. I don’t imagine the patient will last long, but does it really matter? He is facing a long depressing death, and I imagine that being the first pioneer in this new and rather spectacular procedure could seem very attractive to him – go out with a big bang and not a whimper.

Now then, would I go for it? In his position I think I probably would. In years to come, if the procedure becomes as routine as having a new heart, I would certainly see it as a life enhancing opportunity. I am 64 now, and beginning to feel it. Why would I not welcome the chance to have a younger, fitter body where all the parts work as they should, and where I would no longer have to put up with all the little aches and pains that come along as you get older? I think I could cope with that. I live in my head – the rest is there just to keep my brain alive.

But where will they get the donors from? I would imagine that a fully functioning but brain dead body is quite a hard thing to find.

 
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Topic: Serious Discussion / Logic Puzzle

There are two guarded doors. Behind one of the doors is pile of gold. Behind the other is a poisonous snake. You may ask only a single question to one of the two guards. Unfortunately, one of them always tells the truth and the other always lies. (You do not know which is which.)

Assuming that each guard is aware of the other’s truthfulness or mendacity, you ask each either guard “if I asked the other which door conceals the gold, which door would he point to?” They will both point to the door with the snake, so you choose the other one.

The second one may take a little longer!

 
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Topic: Serious Discussion / Logic Puzzle

There are three kinds of people – those who can count and those who can’t.

 
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Topic: Serious Discussion / Logic Puzzle

IOD, there won’t be any grain to collect if you leave it with the goose.

 
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Topic: Serious Discussion / Logic Puzzle

You also have to include 100 and 001 in the success list. That give you six winners and two losers, 75% chance of success.

 
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Topic: Serious Discussion / Logic Puzzle

BSG can explain that :)

 
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Topic: Serious Discussion / Logic Puzzle

How do you get all three things safely across the river and to the market?

You take the goose first. The fox won’t eat the grain. You then go back and take either of the other two passengers. At the other side you leave the second item and put the goose back in the boat. Go back to the start, leave the goose and collect whatever was left. Take it to the other side, once again leaving the fox with the grain. Finally you can go back to the start and fetch the goose.

 
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Topic: Serious Discussion / Logic Puzzle

If they’re wearing the same hat color, B forfeits and then C can simply state the hat color of A as their own.

Agreed.

If B does not forfeit, C can state the opposite color as A is wearing, providing for all 4 of the scenarios.

If B does not forfeit, that means he has guessed. He can guess or pass, that’s it. If he guessed right, they all go free. If he guessed wrong, they all die. Either way C doesn’t get a turn.

edit. I hadn’t seen your last post. Yes, there has to be one correct guess in the game. If a player passes, that’s it. He can’t go back and have another turn.

 
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Topic: Serious Discussion / Logic Puzzle

Yes, I see what you’re getting at here. You’re actually proposing a new optimal strategy. I’ve known this one for years, and nobody has ever done that before, which is interesting; I’ll have a little think about this.

 
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Topic: Serious Discussion / Logic Puzzle

(If they are not wearing the same color)
If two people pass, the sole person that guesses knows their hat is the other color and the guess is easy.

Yes, you’re right here. If player C sees two red hats and the other players pass, C can deduce that he must be wearing a blue hat.

(If they are all wearing the same color)
If everyone guesses, they are all wearing the same color and the guess is easy.

But you’re wrong here. They can’t all guess. Player A will play optimal strategy, choose the other colour, AND LOSE THE GAME. There can be no further guesses, it’s all over at that point.

 
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Topic: Serious Discussion / Logic Puzzle

Yeah I don’t know how to explain it to you any other way, everyone having the same colored hat would not mean the strategy doesn’t work. If B sees that A and C have the same color, he doesn’t say anything. C then knows that his hat is the same color as A’s.

Except that B doesn’t get the opportunity. In the case of three red hats, A sees two red hats and chooses blue for himself (using optimal strategy). He is wrong and loses.

If you break ranks and try to be clever with this one, the six winning possibilities evaporate. This really is a very simple probability problem – there are six winning combinations and two losers. Choosing is ALWAYS a risk.

 
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Topic: Serious Discussion / Logic Puzzle

Passing simply reveals that that player can see one hat of each colour. It still doesn’t tell the third player what colour is on his own head.

There is no guaranteed win. There are eight possible arrangements of hats. Two of them are all red or all blue. In that case, the first prisoner chooses the other colour and loses.

The other six are two of one colour and one of the other. So in those arrangements only one prisoner can see two identical hats. He chooses the other colour and wins. So using optimal strategy and ignoring lucky guesses, six possibilities out of eight set them free, the other two see them die. The chances of winning are 75%.

 
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Topic: Serious Discussion / Logic Puzzle

There are eight possible arrangements for the hats:-

A blue blue blue red red red red blue

B blue blue red red red blue blue red

C blue red red blue red red blue blue

Of these, bbb and rrr are fatal. In the other six arrangements any man seeing two hats the same colour guesses that his is the opposite colour, and wins. This is assuming optimal strategy and not just a lucky random guess. So their chances of survival are 75%.

 
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Topic: Serious Discussion / Logic Puzzle

Well, their chances of survival are 50% then if they cannot share information.

No they aren’t.

it’s 100% if they follow the strategy BSG outlined above

Also wrong. If they are all the same colour, then the third man must either guess, which is bound to be wrong, or pass, in which case there are no correct answers and they all die.

 
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Topic: Serious Discussion / Logic Puzzle

Pete, passing and forfeiting are the same thing.

The question is what are their chances of survival. You don’t actually need to work out what each one sees and what he says.

 
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Topic: Serious Discussion / Logic Puzzle

They can make a guess or forfeit their turn. I didn’t say they could have a conversation. Try again.

 
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Topic: Serious Discussion / Logic Puzzle

OK then, more hats. This one’s actually quite easy if you think about it.

Three condemned men enter the death chamber. The executioner then tosses a coin three times and places either a red or a blue hat on each prisoner’s head, according to the result of the toss. Each prisoner can see the colour of the other two men’s hats, but not his own.

They are then told that they can either make a guess as to the colour of their own hat, or they can forfeit their turn. If one man guesses correctly, and there are no wrong answers, they will all be pardonned and set free. Any wrong guesses will see them all hang.

What are their chances of survival if they optimise their strategy?

 
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Topic: Serious Discussion / Logic Puzzle

Yes, I rather like it when puzzles have more than one solution. I’ve already done one, so it must be karma’s turn.

I try these sorts of puzzles on other people all the time. I remember one which I haven’t seen for ages, which I believe was one of Martin Gardner’s. It involved Tweedledum and Tweedledee, and two watches which kept very bad time. I think the puzzle was to figure out which of the twins was older, and it was very ingenious. Anyone know what I’m talking about?

 
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Topic: Serious Discussion / Logic Puzzle

Or they could be on separate treadmills.