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 Sadly, though
not unexpectedly, no solutions have been forthcoming for the billiard
ball problem we set in Issue 4. Mind you, it's no snack, even for people
used to doing puzzles. Which explains some of the questions readers have
raised, like the following:
Does
the problem demand that we not know at the start if the odd ball is
lighter or heavier? (afraid so)
How
many should I weigh at a time — twelve, eight, six? (a crucial
question, this one)
Is
it all trial and error to arrive at a solution? (for me, yes — I know
of no algorithm for solving such problems).
Apart
from the question of how many to weigh, the solution does require a
certain amount of lateral reasoning — not cheating, just sneaky
thinking.
But the most
important point is to realise that all possible outcomes have to be
allowed for (such as "what does it mean if the balls we happen to
weigh this time balance?"). Computer programmers will know this
approach — and its frustrations, because in that game you always have
to cater, in advance, for all eventualities.
In the absence of
any other, then, my own solution, in a hopefully easy to understand
layout, may be found here.
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