On 6/5/07, Andrew Nikitin <[EMAIL PROTECTED]> wrote
Here is a puzzle for your enjoyment. I saw it recently and it was new to me.
I am not sure I would have solved it if I hadn't used J.
If I understand your puzzle statement correctly, it's equivalent to
Define strategy where
setup=: *./@(= 1 (''$strategy)\. ])@:[EMAIL PROTECTED]
setup 88
must always return true. (I've changed the numeric range from 1..88
to 0..79, but that doesn't change the nature of the problem.)
It seems to me that any strategy that works for setup 88 should also
work for setup 2.
This becomes equivalent to the problem:
a is 0 or 1,
b is 0 or 1
find a function of a and b such that a=f(b) OR b=f(a)
In other words, a winning strategy should also deal with the cases:
a b
0 0
0 1
1 0
1 1
It seems to me that this has no good answer, since a and b
vary independently -- knowing a tells you nothing about b, and
knowing b tells you nothing about a.
I suppose we might also include a "person index" as a parameter
for this function. But, that doesn't give you any further information.
Unless we introduce some new element into the problem (for example:
I see nothing in the rules which prohibits people from inspecting
all the hats beforehand, whereupon they could all agree to pick the
number on the smallest valued hat -- but this presumes that there
are only 88 hats, and I don't see that guaranteed, either), I don't think
a win can be guaranteed..
--
Raul
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