They can guarantee all except one to be saved (and this holds for as many
gnomes as are in the line). The first gnome has no information, and must
definitely guess his color, so cannot be guaranteed his life. But, if he
states 'red' if there are an odd number of red hatted gnomes in front of
him, and 'white' if there are an even number of red hatted gnomes in front of
him, then everyone else can be saved. For example, if he says 'red,' then
that means there are 1,3,5,7 or 9 red gnomes in front of him. The gnome
directly in fornt of him sees either that same number or reds, or one
less (an even number). If he sees one less then that means he is a red, and
if the number is the same then he is white. Everyone else can listen to
this going on and count the number (odd or even) of reds in front of him,
and compare it to the data the gnome behind him gives.
This page was last modified on 12/14/99. Copyright me