
the VisualText Art Venue
David Colosi
Exercise in Active Reading 
Twelve balls exist. They are all of equal weight except for one which
is either heavier or lighter than the others. Find the ball of different
weight by weighing the balls only three times on a balance. Weigh four balls
against four. If the scale is balanced eliminate all eight balls. Next weigh
two of the remaining four balls against each other. If the scale is balanced
then eliminate one of the balls on the scale and weigh one of the others
against the ball on the scale. If the scale is balanced again then the ball
that remained off the scale is Odd. If the scale is imbalanced then the
most recent ball placed on the scale is Odd. If the scale is imbalanced
after weighing two of the remaining four balls against each other then remove
one and record it. Then weigh one of the remaining balls against the ball
on the scale. If the scale is balanced then the ball that was removed is
Odd. If the scale is imbalanced then the ball that initially remained on
the scale is Odd. If the scale is imbalanced after weighing four balls against
four balls then the Odd ball is on the scale. Replace three of the known
Even balls (now off the scale) with three of the balls on the right side
of the scale. Then take the three balls from the right side of the scale
and replace them with three on the left side. Leave the three from the left
side out. If the scale is imbalanced in the same direction then the odd
ball is one or the other of the two balls that didn't change positions.
Weigh one of those against a known Even ball to find the Odd one. If the
scale is imbalanced in the opposite direction then you know that you've
moved the Odd ball to the left side. You also know whether the Odd ball
is heavy or light depending on how the scale changed. Weigh two of the possible
Odd balls against each other, and if the scale is balanced then the Odd
ball is the one not on the scale, but if it is imbalanced, the Odd ball
is the one of the known weight difference. If the scale is balanced after
the three ball rotation then the Odd ball is not on the scale. You also
know whether the Odd ball is heavy or light from the orientation you found
after initially weighing four balls against four. Again weigh two of the
possible Odd balls against each other, and if the scale is balanced then
the Odd ball is the one not on the scale, but if it is imbalanced, the Odd
ball is the one of the known weight difference.
