Room A is full of gnomes who all have their standard pointy hats on, but an evil
sorcerer has glued all their hats to their heads and changed some of their hats
from the usual red to blue...
(i.e. room with N gnomes of which N - X have red hats on and X have blue.)
No gnome knows the colour of his own hat
Room B is connected to room A with a door and is currently empty. Neither rooms
have anything notable (like mirrors) to aid the gnomes finding out their hat
colour.
The sorcerer has set a challenge - the gnomes must go one by one through the
door to the other room and once all gnomes have gone through to room B they must
be standing in two groups sorted by hat colour (i.e. all the reds in one group
and all the blues in the other).
Unfortunately the sorcerer has also set some restrictions...
The gnomes are not allowed to communicate with another in any way(no words,
winks, head-shaking or anything else!).
You are allowed to help them, BUT you are allowed only one sentance to help
them. You can tell this one sentance to each individual gnome or to the group
as a whole. The sentance will be the same regardless of both the total number
of gnomes and the proportion of gnomes with each hat colour (Assume you are
telling them over an intercom!)
The sentance is short, the solution logical and it causes the gnomes to sort
themselves into one group of red and one group of blue hat wearers!
(and if you fail the sorcerer will turn YOU into a blue-hatted gnome as well!
;-) )
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