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 The many sages (Posted on 2004-04-13)
This is a generalisation of "The three sages"

On a hot summer day, n equally bright philosophers, tired from all that philosophising, were napping in an orchard. A prankster came by, and painted all of their faces black with charcoal.

When the philosophers woke up, they started laughing at the others... until they suddenly realised all of their faces must be black!

How did they come to that conclusion?

 Submitted by e.g. Rating: 2.3636 (11 votes) Solution: (Hide) If n=2, both could have thought "If my face is clean, what's the other laughing at? Therefore, my face must be black." If n=3, each could have thought: "If my face is clean, why are the other two laughing? They should apply the 'n=2' case, and stop laughing; since they don't, my face must be black, too." In general, for P philosophers, each would think ""If my face is clean, why are the other (P-1) laughing? They should apply the 'n=(P-1)' case, and stop laughing; since they don't, my face must be black, too."

 Subject Author Date hint Goldensky 2007-02-24 06:16:25 Solution David Piccolo 2004-05-06 05:39:13 solution? shaily 2004-04-29 12:42:21 solution? luke 2004-04-27 23:01:48 On a hot summer day... Sing4TheDay 2004-04-21 10:04:48 WHY??? Karlo 2004-04-18 03:16:44 Looking at Case N is easier by looking back at case n. Joshua 2004-04-17 02:32:37 Simple Solution, I think... jon&lilet 2004-04-16 04:36:29 re(2): Many Sages -ragge- 2004-04-15 17:10:08 n philosophers JCD 2004-04-14 20:22:51 A hot summer day Wendy 2004-04-14 12:52:54 sage barrage prince 2004-04-14 11:52:40 The puzzle re-worded Penny 2004-04-13 14:33:38 re: Many Sages Charlie 2004-04-13 14:10:09 But what would happen if... Charlie 2004-04-13 14:08:02 Many Sages Brian Smith 2004-04-13 14:05:04 re(4): Is there something funny about a black face ? Penny 2004-04-13 13:51:06 re(3): Is there something funny about a black face ? Federico Kereki 2004-04-13 13:45:20 re(2): Is there something funny about a black face ? Penny 2004-04-13 13:40:55 re: Is there something funny about a black face ? Federico Kereki 2004-04-13 12:39:30 Is there something funny about a black face ? Penny 2004-04-13 12:19:41 re: Inductively Federico Kereki 2004-04-13 10:51:23 Inductively Oskar Hund 2004-04-13 10:47:56 Solution? sassy 2004-04-13 09:52:03

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