There are$ 1$ cm long bars with a number$ 1$, $2$ or $3$ written on each one from them. There is an unlimited supply of bars with each number. Two triangles formed by three bars are considered different if none of them can be built with the bars of the other triangle. (a) How many different triangles formed by three bars are possible? (b) An equilateral triangle of side length $3$ cm is formed using $18$ bars, , divided into $9$ equilateral triangles, different by pairs, $1$ cm long on each side. Find the largest sum possible from the numbers written on the $9$ bars of the border of the big triangle.