Problem 189A — Cut Ribbon
The problem is to maximize x+y+z subject to ax+by+cz=n. Constraints are low, so simply iterate over two variables (say x and y) and find the third variable (if any) from the second equation. Find the maximum over all feasible solutions.
Other approaches: Use dynamic programming with each state being the remainder of ribbon. Select the next piece to be a, b or c.
Problem 189B — Counting Rhombi
Observe that lots of rhombi have the same shape, but are in different locations.
What uniquely determines the shape of a rhombus? Its width and its height.
Is it possible to build a rhombus with every width and every height such that the vertices of the rhombus are in integer points?