eirik@tekchips.UUCP (Eirik Fuller) (03/10/86)
Thanks to all who replied to my posting. The answer has already been posted, but I thought I would add a few comments. One posting gave the definitive example for the ultimate skeptic. Steve Villee pointed out that with the front wheel perpendicular to the back wheel, the back wheel doesn't move at all. This example is what I used originally to convince myself of the answer. (No flames; do you do your best thinking while chugging up a steep hill? I find thinking passes the time, but that doesn't mean I do it well.) Most of the people who responded got the answer right. Only one person, Dave "The Peddler" Richards, commented on the quality of the puzzle: "I had to think about this one awhile. Excellent puzzle! Your hint made the difference, though." He was also the only counterexample to my initial suspicion that the answer came quickly if at all. The only real obstacle, for those who didn't get it, is realizing the relevance of the fact that the front wheel steers. The funniest response I got, from Ken Brown: I don't know what the difference both tires travelled would be, but it won't be very much. (unless you ride in circles alot :-) One more comment: if the slippage assumption is removed, the answer is complicated by the fact that slippage can occur in both directions. In my experience backwards slippage (which decreases the mileage) is more common than forward slippage. In particular, the fixed gear I was riding when I thought of the puzzle slips a lot when I stop it without brakes (though I'm getting better at brakeless stopping without skidding). Yes, it does have brakes, for panic stops in traffic (I'm crazy, but not THAT crazy).