perplexus.info :: Logic : The many sages

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."

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-03-16 10:26:12
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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