Question 42
There are sticks of length $1$ with a number $1$, $2$ or $3$ written on each of them. There is an unlimited supply of sticks with every number. Two triangles consisting of three sticks are considered different if neither of the triangles can be composed from sticks of the other triangle.
a. How many different triangles consisting of three sticks are possible?
b. From $18$ sticks, one makes an equilateral triangle of side length $3$, divided into $9$ pairwise different equilateral triangles of side length $1$. Find the largest possible sum of the numbers written on the $9$ sticks on the boundary of the big triangle.
a. How many different triangles consisting of three sticks are possible?
b. From $18$ sticks, one makes an equilateral triangle of side length $3$, divided into $9$ pairwise different equilateral triangles of side length $1$. Find the largest possible sum of the numbers written on the $9$ sticks on the boundary of the big triangle.