Given n > 1 items and a two pan balance scale with no weights, determine the lightest and the heaviest items in $\lceil 3n/2 \rceil − 2$ weighings. I tried splitting down the middle and picking one side over the other given some condition, but I'm not able to properly define the conditions.
A simple way to find the heaviest object is to compare two object keep only the heaviest and repeat until you compared all object.
Problem of this method : $n-1$ comparison needed for the heaviest (and as much for the lightest).
However to meet your bound only a small improvement is needed.
Divide and conquer
Be clever when dividing
$n/2$ comparison is clever enough ;)
$$3n/2-2 = n/2+(n/2-1)+(n/2-1)$$