Question number four. Peter made a map of his town. He drew on it all four streets, all seven intersections, and the houses of four of his friends. In reality, straight streets, skew street, and long street run along straight lines. The fourth street on the map is wavy street. Which of Peter's four friends lives on wavy street? Let's study the intersections and let's make a tally of all the possible intersections in town denoting the names of the streets by the first letters of the boy that lives on that street. So we have the possibility of A intersecting with B, with C, and with D, B intersecting with C and D, and finally C intersecting with D. So looking at the map, we have an intersection here between A and D, and an intersection between A and C here and here, then an intersection between B and C in two places, an intersection here between D and C here, an intersection between B and D, and that's it. So A and B do not intersect. And then we recall from geometry that unless the lines have infinitely many intersections, so they're the same line essentially, which will not happen on a street map, there is the possibility of them intersecting once or not at all. So here for A and C, we have a problem, and for B and C, we have a problem with two intersections. So suppose that A is not a straight street. In that case, here we have that B or C is also not straight, which is a problem because we're only allowed to have one wavy street. Well, if we suppose that B instead of A is the wavy street, then we have one, and it doesn't here account for A or C also being wavy, so that's a problem. But if we let C be the street that's called wavy street, then it can intersect both A and B, and that's not a problem for a line that's not straight. So having eliminated A and B, we conclude that C has to be wavy street.

Wavy Street

intersections

Peter's map

street C

anomalies