# Cool Problem

Let $$f(n)$$ denote the sum $$1+2+3+...+(n−1)+n$$. Let $$g(n)$$ denote the sum $$1+3+...+k$$, where $$k$$ is the $$n$$th positive odd number. There are $$x$$ integers n such that $$1≤n≤100$$ and $$2f(n)−g(n)$$ is divisible by both $$3$$and $$2$$. What is the sum of the digits of $$x$$?