stevev@tekchips.UUCP (Steve Vegdahl) (02/20/84)
> Consider the vector from the AxeWielder to the center of the lake. > Paddle in the direction of the vector. This will get you further from > the center; this guarantees that you will eventually reach the shore. > It also keeps the center of the lake between you and the AxeWielder; > this guarantees safety. > Step 2 is a loop with the invariant ``The center is between me and the > AxeWielder''. The termination function is the distance to the shore. > Step 1 is initialization. I believe that the Gary gives is incorrect, as it makes no use of the ratio of the speeds of the Axe-man and woman. His argument would be equally (in)correct if the Axe-man could paddle 1,000,000,000 times as fast as the woman could row. The woman would end up going approximately in a circle around the middle of the lake. The invariant will certainly not hold in this case. I hacked up a computer simulation that suggests that the woman would indeed fail to reach the shore using Gary's method. I still believe that my previously-posted solution (moving away from the Axe-man 0.25 across the lake and then bolting) works. Steve