All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 All dogs are the same color! (Posted on 2003-05-30)
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)

 Subject Author Date Error! Math Man 2011-10-13 20:59:15 k = 1 Bractals 2005-02-16 01:15:35 error....... cat 2005-02-15 00:04:51 The obvious error FB 2004-11-30 07:07:07 No Subject Hattie 2004-11-24 18:25:22 Misuse of induction Jeff 2003-12-23 20:42:46 don't get it michelle 2003-11-11 18:17:03 Calling the k9 corps !!!!!!! Dan 2003-09-19 19:20:11 What Lawrence 2003-08-28 22:04:20 Furthermore Stuart 2003-08-06 21:33:58 Simpler solution Stuart 2003-08-06 21:28:54 huh? mullen 2003-06-21 03:15:31 Dunno Tim Axoy 2003-06-08 02:32:58 re(2): dogged logic Gamer 2003-05-31 06:12:04 re: dogged logic pleasance 2003-05-31 00:58:27 Solution? Maybe... Pickels 2003-05-30 19:08:25 dogged logic mark hartman 2003-05-30 11:55:05 re: solution TomM 2003-05-30 10:56:09 re: solution Gamer 2003-05-30 10:41:28 solution Charlie 2003-05-30 10:22:18 Possible flaw? Gamer 2003-05-30 10:16:36 re: My thoughts. Charlie 2003-05-30 10:14:59 My thoughts. Bryan 2003-05-30 10:04:49

 Search: Search body:
Forums (0)