Among \(12\) identical-looking balls, exactly one has a different weight (we do not know whether it is heavier or lighter than the others).
Using a balance scale, show how to determine the odd ball, and whether it is lighter or heavier, using only three weighings.
Three positive numbers \(a,b,c\) satisfy \(ac-bc+ab=63\). What is the smallest value that \(a^2+b^2+c^2\) can be?
Among \(9\) identical-looking balls, exactly one has a different weight. We do not know whether it is heavier or lighter than the others.
Show that it is possible to find the odd ball, and also tell whether it is heavier or lighter, using only \(3\) weighings on a balance scale.
Among \(27\) identical-looking balls, exactly one is heavier than all the others.
Show that it is possible to find the heavier ball using only \(3\) weighings on a balance scale.