13th Canadian Mathematical Olympiad Problems 1981

13th Canadian Mathematical Olympiad Problems 19811.  Show that there are no real solutions to [x] + [2x] + [4x] + [8x] + [16x] + [32x] = 12345. 2.  The circle C has radius 1 and touches the line L at P. The point X lies on C and Y is the foot of the perpendicular from X to L. Find the maximum possible value of area PXY (as X varies).