1. How many ways can a domino be placed on a 4 x 4 chessboard? Each "half" of the domino must cover exactly one square of the chessboard. An example is shown below.
2. How many different non-congruent isosceles triangles can be formed by connecting three of the dots in a square array of dots like the one shown below?
Two triangles are congruent if they have the same traced outline, possibly up to rotating and flipping. This is equivalent to having the same set of 3 side lengths.