Statement

In a quiet alley by the old museum, Mira the frame-maker has just received a large shipment of wooden rails. Every rail is exactly one of three lengths: A, B, or C, and she has unlimited supply of each. Mira wants to know how many different rectangles she can make by joining four rails into a frame, where each side must be exactly one of the given lengths. Two rectangles that differ only by rotation (for example, 3 × 4 and 4 × 3) are considered the same rectangle. Squares (where both side lengths are equal) are allowed.