x******a
发帖数: 6336 | 1 In a distant, dark forest, lives a population of 400 highly intelligent
dwarfs. The dwarfs all look exactly alike, but only differ in the fact that
they are wearing either a red or a blue hat. There are 250 dwarfs with a red
hat and 150 dwarfs with a blue hat. Striking however, is that the dwarfs
don't know these numbers themselves and that none of them knows what the
colour of his hat is (there are for example no mirrors in this forest). But
the dwarfs do know that there is at least one dwarf w |
J******d
发帖数: 506 | 2 太经典了。居然连问句都没有。
that
red
But
village,
intended
to
【在 x******a 的大作中提到】
: In a distant, dark forest, lives a population of 400 highly intelligent
: dwarfs. The dwarfs all look exactly alike, but only differ in the fact that
: they are wearing either a red or a blue hat. There are 250 dwarfs with a red
: hat and 150 dwarfs with a blue hat. Striking however, is that the dwarfs
: don't know these numbers themselves and that none of them knows what the
: colour of his hat is (there are for example no mirrors in this forest). But
: the dwarfs do know that there is at least one dwarf w
|
x******a
发帖数: 6336 | 3 The Question: How many days does it take before there are no more dwarfs
with a red hat left at the party?
lol
太经典了。居然连问句都没有。
that
red
But
village,
intended
to
【在 J******d 的大作中提到】
: 太经典了。居然连问句都没有。
:
: that
: red
: But
: village,
: intended
: to
|
p*****k
发帖数: 318 | 4 xiaojiya, it's probably the best example to illustrate
the concept of "common knowledge":
http://en.wikipedia.org/wiki/Common_knowledge_%28logic%29
or see Terry Tao's extremely popular blog post:
http://terrytao.wordpress.com/2008/02/05/the-blue-eyed-islanders-puzzle/ |
x******a
发帖数: 6336 | 5 pcasnik, thank you for the link.
the question i have is why
"After nobody commits suicide on the day, each of the blue eyed people then
realizes that they themselves must have blue eyes, and will then commit
suicide on the day. "
【在 p*****k 的大作中提到】
: xiaojiya, it's probably the best example to illustrate
: the concept of "common knowledge":
: http://en.wikipedia.org/wiki/Common_knowledge_%28logic%29
: or see Terry Tao's extremely popular blog post:
: http://terrytao.wordpress.com/2008/02/05/the-blue-eyed-islanders-puzzle/
|
z****i
发帖数: 406 | 6 大牛你太牛了，什么都会，什么都能找到。
忍不住跳出来赞一下。 ：）
【在 p*****k 的大作中提到】
: xiaojiya, it's probably the best example to illustrate
: the concept of "common knowledge":
: http://en.wikipedia.org/wiki/Common_knowledge_%28logic%29
: or see Terry Tao's extremely popular blog post:
: http://terrytao.wordpress.com/2008/02/05/the-blue-eyed-islanders-puzzle/
|
f********y
发帖数: 278 | 7 从LZ问题里看不出这个逻辑能适用，尽管和heard on the street里面的那个妻子把偷
情的丈夫踢出家门的例子类似。
then
【在 x******a 的大作中提到】
: pcasnik, thank you for the link.
: the question i have is why
: "After nobody commits suicide on the day, each of the blue eyed people then
: realizes that they themselves must have blue eyes, and will then commit
: suicide on the day. "
|
p*****k
发帖数: 318 | 8 WARNING: long and probably non-sense
(better off reading the links pointed above)
xiaojiya, i really cannot do a better job explaining this
than t.tao (or wikipedia). i think most ppl would be satisfied
to understand the induction proof, but as tao pointed out, the
paradox is that it seems the info from the outsider provides
no extra info (if there are more than one blue-eyed islander)
the way to resolve it is to realize that, what the outsider said
was only "kth-order knowledge" if there are
【在 x******a 的大作中提到】
: pcasnik, thank you for the link.
: the question i have is why
: "After nobody commits suicide on the day, each of the blue eyed people then
: realizes that they themselves must have blue eyes, and will then commit
: suicide on the day. "
|
l******u
发帖数: 1174 | 9 250 days.
that
red
But
village,
intended
to
【在 x******a 的大作中提到】
: In a distant, dark forest, lives a population of 400 highly intelligent
: dwarfs. The dwarfs all look exactly alike, but only differ in the fact that
: they are wearing either a red or a blue hat. There are 250 dwarfs with a red
: hat and 150 dwarfs with a blue hat. Striking however, is that the dwarfs
: don't know these numbers themselves and that none of them knows what the
: colour of his hat is (there are for example no mirrors in this forest). But
: the dwarfs do know that there is at least one dwarf w
|
x******a
发帖数: 6336 | 10 我想知道他们可以看到249个还是只看到一些而不知道有249个。 |
