Little Suzy has a tricycle (you know, with three wheels). She wants to travel 1 mile with the tricycle, but she wants to spare her tyres (you know the price on tricycle tyres just keep going up). She is taking 2 spare tyres.

Assume she knows when to exchange wheels so that each of them travels an equal distance. How far does each wheel travel at the end of one mile? How did she exchange the wheels?

Please forgive the following anecdote, fear not, I will eventually tie it into some kind of solution.
When I was around 12 my friends odd-ball father (his list of oddities belongs in a book, not this post) bought a huge shopping tricycle to go with his Sinclair C5 (“the future of travel”) and his dilapidated milk-float (which he ‘promised’ us he would take us to school in when it was ‘fixed up’ – which thankfully it never was)
You would think they are the easiest things in the world to ride – huge wheels, triangular ‘feet’ (so can’t possibly wobble – why aren’t all pub tables on tripods?), designed for ‘oldies’ – easy right?
Wrong. They’re far from easy when you first get on.
They’re impossible to keep in a straight line! It didn’t help the brakes were keen as mustard, so as soon as you started to peddle (and hence veer hazardously towards the main road) the brakes you hit in panic shook your very soul.
We walked it to the local park for a bit of practice.
**The facial expression I now reserve for nonchalance (to mask fear and embarrassment) was formed on that walk.**
After an hour we were making progress. A straight line for a quarter mile was possible with enough concentration, but was inconsistent and very slow.
Then the fun began. My friend nearly jackknifed the bike and in his panic popped up on the two side wheels for a full revolution of the pedals!
Somehow he had made this bike look almost cool!
After that it was almost too easy – simply give in to the veer of the bike on the first pedal – snap the handlebars and you were up on two wheels!
With the fear gone riding this thing on 2/3 of its full compliment was almost as easy as riding a traditional bike – and if it didn’t strictly look cool it certainly felt it.
We enjoyed that bike for the almost all of the remainder of the summer break. Our fun was cut short after I has a reasonably bad accident on it due to a gnarly manhole (shock absorbtion=0) and a Volvo.
Ironically it was one of the rare occasions I was riding on all three wheels.

So here is my solution.
Lucy decides it is much more fun to ride on two wheels anyhow, and besides, her rear left tyre is as bald as the author of the above anecdote. She takes two spare tyres – swaps them front and back-right at the halfway mark and enjoys the rest of her journey keeping a close eye out for the smarter-mouthed kids at her school.
Oh, and Volvos.

Posted by Lee on 2004-02-24 12:06:02