### 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?