|
Consider an object such as a triangle. The triangle has 3 sides, an odd number of edges. If you put your pencil down on the outside, and cross all 3 edges, you'll wind up back inside the triangle. Similar, if you put your pencil down on the inside of the triangle, you'll wind up back on the outside of the triangle. Now, the reason for this is that there is an odd number of edges. The box shown has 3 squares with an odd number of edges, namely 5 edges. Note that it doesn't matter that the 3 squares are adjacent. (The 2 squares on the top right and the top left are irrelevant because they have an even number of edges.)
Now recall from the triangle example that if you start outside of the triangle that you will have to end up on the inside of the triangle to cross every edge exactly once. But yet we have 3 squares with an odd number of edges to cross!
We cannot start on the outside of any of theses particular squares, and end up back inside the other 2 squares at the same time(when we start from a point inside one of the squares, we have started from a point outside the other 2 squares and must end up inside both of those to complete the puzzle). Thus the task is impossible because you cannot be on the inside of the remaining 2 squares at the same time! |
