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jack1. St Ives
As I was going to Saint Ives,
I met a man with seven wives
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits
Kits, cats, sacks and wives
How many were going to Saint Ives?
Which way was the man going? Let's say 'from saint Ives', because that's traditional, ignoring the fact that I've certainly met people going the same way I'm going before, and that he might have been going to the *other* st ives.
Did he have his wives with him? Normally 'a man with seven wives' means he married them, not that they're there, but again tradition dictates they were with him. The version I saw cleverly bypassed these two by showing a picture, which clearly showed the man driving in the opposite direction with a cat-laden wagon.
So the tradtional answer is 'One. You.' But it seems obvious to me that the last two lines are asking 'how many kits, cats, sacks and wives', to which the answer would be 'none' making the same assumptions[1].
And finally, for the record, there are 7^4+7^3+7^2+7^1+7^0 mammals in his car.
[1] Yeah, there may be *other* cats going to saint ives, but that's not what it says.
2. Goats
"Three doors. One car. Two goats. You want the car. You choose a door. Monty Haul opens another door he knows to have a goat behind, and allows you to open your door, or the other one."
Switch, giving you a 2/3 chance: WLOG suppose the order is CGG, and you chose door n. If n is 1, you lose by switching (whether M opens 2 or 3), and if n is 2 or 3, you lose by not switching (M has opened the other one), giving switching a 2/3 chance of winning.
However, a large (though by no means largest) part of the confusion is that lots of people phrase the question differently. If Monty opens a door *he knows to have a goat*, the calculation works as described. If he opens a door at random, which *happens* to have a goat, then the normal analysis of "it doesn't matter, it's 1/3 either way, I mean 1/2" is correct, the other 1/3 being the one that didn't happen, him opening the car door and going 'whoops'.
What's worst is when the question says "he opens a door which has a goat behind" when it could be either interpretation, and you face the 'random but not uniform' problem which means it's basically unsolvable. In this case you could arbitrarily decide he opened a door at random, but that would fail miserably for indeterminates like "he put an integer amount of money in an envelope."
3. Yolks
"Is it more correct to say 'the yolk of an egg is white' or 'the yolk of an egg are white'?"
It's *more* correct to say 'is white' because that's grammatically correct and factually false, and the other is wrong both ways. If the question was "Is it correct to say..."[2] the answer would be 'mu'. Of course, in casual conversation the answer is "is yellow", but for a puzzle you should answer the question asked, shouldn't you?
[2] I've always heard 'more correct', I don't know what everyone else has...
As I was going to Saint Ives,
I met a man with seven wives
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits
Kits, cats, sacks and wives
How many were going to Saint Ives?
Which way was the man going? Let's say 'from saint Ives', because that's traditional, ignoring the fact that I've certainly met people going the same way I'm going before, and that he might have been going to the *other* st ives.
Did he have his wives with him? Normally 'a man with seven wives' means he married them, not that they're there, but again tradition dictates they were with him. The version I saw cleverly bypassed these two by showing a picture, which clearly showed the man driving in the opposite direction with a cat-laden wagon.
So the tradtional answer is 'One. You.' But it seems obvious to me that the last two lines are asking 'how many kits, cats, sacks and wives', to which the answer would be 'none' making the same assumptions[1].
And finally, for the record, there are 7^4+7^3+7^2+7^1+7^0 mammals in his car.
[1] Yeah, there may be *other* cats going to saint ives, but that's not what it says.
2. Goats
"Three doors. One car. Two goats. You want the car. You choose a door. Monty Haul opens another door he knows to have a goat behind, and allows you to open your door, or the other one."
Switch, giving you a 2/3 chance: WLOG suppose the order is CGG, and you chose door n. If n is 1, you lose by switching (whether M opens 2 or 3), and if n is 2 or 3, you lose by not switching (M has opened the other one), giving switching a 2/3 chance of winning.
However, a large (though by no means largest) part of the confusion is that lots of people phrase the question differently. If Monty opens a door *he knows to have a goat*, the calculation works as described. If he opens a door at random, which *happens* to have a goat, then the normal analysis of "it doesn't matter, it's 1/3 either way, I mean 1/2" is correct, the other 1/3 being the one that didn't happen, him opening the car door and going 'whoops'.
What's worst is when the question says "he opens a door which has a goat behind" when it could be either interpretation, and you face the 'random but not uniform' problem which means it's basically unsolvable. In this case you could arbitrarily decide he opened a door at random, but that would fail miserably for indeterminates like "he put an integer amount of money in an envelope."
3. Yolks
"Is it more correct to say 'the yolk of an egg is white' or 'the yolk of an egg are white'?"
It's *more* correct to say 'is white' because that's grammatically correct and factually false, and the other is wrong both ways. If the question was "Is it correct to say..."[2] the answer would be 'mu'. Of course, in casual conversation the answer is "is yellow", but for a puzzle you should answer the question asked, shouldn't you?
[2] I've always heard 'more correct', I don't know what everyone else has...
no subject
Date: 2005-05-13 05:54 pm (UTC)