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All dogs are the same color! (Posted on 2003-05-30) Difficulty: 3 of 5
Find the mistake in the following proof that all dogs are the same color (if there's any):

Let's use induction. Consider groups of 1 dog. All dogs of every group are the same color, of course. So we now that it's true for 1. Suppose it's true for groups of k dogs, i.e. every group of k dogs are the same color. Then let's consider any group A of k+1 dogs. Consider a subgroup of A containing k dogs. Let's call x the dog in A but not in the subgroup. Then by induction, all dogs in the subgroup are the same color. Now consider a subroup of A of k dogs, with x in the subgroup. All dogs except for x are the same color. Then, since every group of k dogs are the same color (by induction), all dogs in A are the same color. So x and every dog are the same color.

See The Solution Submitted by Fernando    
Rating: 3.5000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
huh? | Comment 12 of 23 |
okay i'm not a genius by any stretch but can i say HUH????????????? you lost me on Let's
  Posted by mullen on 2003-06-21 03:15:31
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