MC part deux
The Dean has determined that mathies have outgrown the building that has served them so well for many years. Luckily for him, the PM has decided to stimulate the economy by funding a new math building. To maximize the stimulating effect, the construction process is outsourced to a software engineering consultant who employs agile methodologies. The building will be built first, and designed later. The Dean has some concerns about this innovative process. After all, it would be very embarrassing if the walls of the new math building failed to line up at right angles!
The Dean sneaks out one night with a tape measure to survey the last remaining grassy area on campus, where the new building will go. He drives stakes into the ground, then measures the distances between them. Afterwards, he retreats into his office to construct a map from his measurements. He notices that the first three stakes form a right-angled triangle with arms of length one metre and hypotenuse of length sqrt(2) metres. And that's not all. The Dean plots these first three stakes on a piece of graph paper at coordinates (0,0), (0,1), and (1,0). After plotting some of the other stakes, it turns out that all of the stakes happen to be precisely at lattice points (i.e. points with integer coordinates) on the graph paper. Still, plotting all of the many stakes is tedious, so he asks his co-op student (i.e. you) to help out.
1 3 1 3 2 1 2 1 0 0
0 0 0 1 1 0