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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: ( You must be logged in to post comments.)
  Subject Author Date
Error!Math Man2011-10-13 20:59:15
Solutionk = 1Bractals2005-02-16 01:15:35
Some Thoughtserror.......cat2005-02-15 00:04:51
The obvious errorFB2004-11-30 07:07:07
No SubjectHattie2004-11-24 18:25:22
Misuse of inductionJeff2003-12-23 20:42:46
don't get itmichelle2003-11-11 18:17:03
Calling the k9 corps !!!!!!!Dan2003-09-19 19:20:11
WhatLawrence2003-08-28 22:04:20
Some ThoughtsFurthermoreStuart2003-08-06 21:33:58
QuestionSimpler solutionStuart2003-08-06 21:28:54
huh?mullen2003-06-21 03:15:31
DunnoTim Axoy2003-06-08 02:32:58
re(2): dogged logicGamer2003-05-31 06:12:04
re: dogged logicpleasance2003-05-31 00:58:27
Some ThoughtsSolution? Maybe...Pickels2003-05-30 19:08:25
dogged logicmark hartman2003-05-30 11:55:05
re: solutionTomM2003-05-30 10:56:09
re: solutionGamer2003-05-30 10:41:28
SolutionsolutionCharlie2003-05-30 10:22:18
QuestionPossible flaw?Gamer2003-05-30 10:16:36
re: My thoughts.Charlie2003-05-30 10:14:59
My thoughts.Bryan2003-05-30 10:04:49
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