Question

You have 13 balls which all look identical. All the balls are the same weight
except for one. Using only a balance scale, can find the odd one out with only 3
weighings? Is it possible to always tell if the odd one out is heavier or lighter than
the other balls?

Answer 1

It is always possible to find odd ball in 3 weighings and in most of the cases it is
possible to tell whether the odd ball is heavier or lighter. Only in one case, it is
not possible to tell the odd ball is whether heavier or lighter.
1. Take 8 balls and weigh 4 against 4.
o If both are not equal, goto step 2
o If both are equal, goto step 3
2. One of these 8 balls is the odd one. Name the balls on heavier side of the
scale as H1, H2, H3 and H4. Similarly, name the balls on the lighter side
of the scale as L1, L2, L3 and L4. Either one of H's is heavier or one of L's
is lighter. Weigh (H1, H2, L1) against (H3, H4, X) where X is one ball from
the remaining 5 balls in intial weighing.
o If both are equal, one of L2, L3, L4 is lighter. Weigh L2 against L3.