FVS wrote:the first riddle is still waiting to be solved.. it is a difficult one , that's true..
It's a nice riddle!
I have kind of a solution which works in most cases but not in all cases. Maybe someone can work out a better solution (and maybe a better way to describe it).
(1)
Put 6 on the scale, 3 left and 3 right.
If the scale is in balance, the 6 on the scale are the reference group (all have the same weight). Name them R. The others contain the fake sac, name them F.
If the scale is out of balance, the 6 which are not on the scale are the reference group (all have the same weight). Name them R. The ones on the scale contain the fake (but you don't know on which side). Name them F.
(2)
Take 3 from R and put them on the left side of the scale.
Take 3 from F and put them on the right side of the scale. Name them X.
Name the remaining ones of F to Y.
If the scale is in balance, Y contains the fake.
If the scale is out of balance, X contains the fake, and you know whether the fake is heavier or lighter!
(3)
You now have a group of three which contains the fake.
Put 2 of them on the scale, one on either side.
If the scale is in balance, the remaining one is the fake.

If the scale is out of balance, and the group was X, the fake is on the scale and you know on which side it is.

If the scale is out of balance, and the group was Y, and the scale was out of balance in (1), the fake is on the scale and you know on which side it is.

If the scale is out of balance, and the group was Y, and the scale was in balance in (1), the fake is on the scale but you don't know on which side
