2014 OIM Problems/Problem 4
Problem
There are 
coins, of which 
are authentic of equal weight and one is false, of different weight than the others. The objective is, using exclusively a two-dimensional scale with dishes, find the fake coin and determine if it is heavier or lighter than the authentic ones. Whenever it can be deduced that one or more coins are authentic, then all those coins are separated immediately and cannot be used in subsequent weightings. Find all for which the objective can be achieved with certainty. (You can do so many weightings as desired.)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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