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Posted by Moby Dick
on 22/9/2009, 8:23 pm, in reply to "Yes. You got it!!"
> Now all you have to do is explain why this works.
Take a look at the truth table:
Perm Bob Alice
CGK . Y .. Y
CKG . Y .. Y
GCK . Y .. Y
GKC . N .. N
KCG . N .. N
KGC . Y .. Y
The only permutations in which Bob fails to get the car are GKC and KCG.
If Bob manages to pick the car first, then Alice must pick either the goat or the key. If she picks the key, she wins. If she picks the goat, she's directed to the key.
If Bob picks the key in door 1 and the car in door 3, then when Alice picks the car, she is directed to the key.
If Bob picks the goat in door 1 and then the car in door 2, then Alice will get the key with her first pick.
Or maybe there's an even simpler way of explaining it? 
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