Springfield Nuclear Power Plant
You are given
4 uranium rods
and you are to discover which
one
of them is faulty. The faulty rod is
either lighter or heavier
than the others. You are also given a scales and a rod of the right mass. What is the
minimum
number of times you have to use scales in order to discover the faulty rod?
The answer is 2.
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1 solution
It can be done in 2 weighings. First, we will take any two rods, say rod A and rod B, and put them on the scales.
If they balance each other, then either rod C or rod D is the faulty rod. We will place rod A and rod C on the scales now. If they balance, then rod D is the faulty rod. If they don't balance, then rod C is the faulty rod.
If rods A and B do not balance each other, then one of these is faulty. We will replace rod B with rod C. If the scales are now balanced, then rod B is the faulty rod. Otherwise, rod A is the faulty rod.
We see that two weighings are sufficient to determine the faulty rod. The faulty rod cannot be identified in just one weighing. □