Never tired bouncing ball
ABCD is a square. Where must the ball hit CD to end up, sooner or later, in A. In the drawing it hits CD 2/3 from D to C and ends up in D.
Problem source: mathschallenge.net.
ABCD is a square. Where must the ball hit CD to end up, sooner or later, in A. In the drawing it hits CD 2/3 from D to C and ends up in D.
Problem source: mathschallenge.net.
March 9th, 2010 at 2:17 am
Does the ball start at A?
March 9th, 2010 at 6:33 am
Yes, always.
March 9th, 2010 at 3:13 pm
You say that, in your example, it /ends up/ at D. That is, once it reaches a corner, we regard its trajectory to have ended. Then it can’t end up at A, for, if it did, its projection onto AB must have made an even number, 2x, of horizontal traversals (from left to right or right to left), and its projection onto AD must have made an even number, 2y, of vertical traversals (from bottom to top or top to bottom). Then halfway through its trajectory those projections had made x horizontal traversals and y vertical traversals, and so it was at a corner, so it got no further.