Logic Puzzle

Here's a puzzle that Zbigniew Michalewicz gave at the Complex Systems 2004 conference in Cairns, though I don't know where he got it from. It was phrased with a lot of redundant information; here's the essential, stripped down version. I think it's quite clever and has an elegant solution (even though I didn't solve it myself :p )

You and a number of other people are seated facing each other in a circle in a plain room, with no prior knowledge of what is about to happen. One person, the host, enters the room, blindfolds everyone seated in the circle, paints a dot of some colour on everyone's forehead, and then removes the blindfolds.
Looking around, you see that multiple colours have been used and that some people, seemingly spaced at random, share the same colour dot as one another.
The host tells you three things:
"You may not communicate in any way the colour of a person's dot."
"I will ring this bell at regular intervals; when I ring the bell, stand up and leave if you know the colour of your dot."
"At some point, you will know the colour of your dot."

The question is, how can you know what colour dot you have?

Hints (in order of revelation - highlight text to read)

1. It is crucial that everyone knows that the problem is solvable.
2. There are an infinite number of colours (but assume for the sake of the problem that you can still tell when two people have the same colour :) ).
3. Can you know what colour you have if you are the only person with that colour?
4. Goto 1.

Yeah, I think everyone who reads this blog has heard this problem anyway, but I still think it's good :p

Useless doctor quota

Brett has had some troubles with doctors. I recently had my useless doctor quota filled at a bulk billing medical centre, too.
I wanted to check on what I had previously thought were two calluses on my foot, but that I had come to suspect may be warts. The doctor, a young timid indian woman, was useless beyond confirming that they were plantar warts.
I asked her what she recommended I do; she said that most people would ask to have them surgically removed; I said I didn't care what most people asked for, I wanted to know what a qualified (I use that term lightly) doctor recommended I should do. I said they weren't causing me any discomfit; she said I could leave it be if I wanted. I said I was concerned about spreading them, given that I do kendo; she said she didn't think that was a problem. I said I'd read that they were contagious and as such there was a small chance of spreading them. She didn't answer my question and instead agreed that normal warts were contagious, when obviously I don't care about normal warts, just plantar warts.
I stopped in exasperation, and flat out asked her "what do you think I should do?". Her answer, which was no answer at all, was that I could do what I liked and if I chose to have them removed I had to make an appointment.
Gah, utterly useless, I still don't know what to do. Ordinarily I'm a very easy going person and don't fault someone for being timid at all. But I think that a doctor cannot afford to be that indecisive. It's one thing to not know the answer; that's perfectly fine, admit it and go find out the answer. It's another thing entirely to try to avoid giving one.

What I Learnt Today

Actually, some cool things I learnt from the first issue of New Scientist that I received the other day:

• Don't use any security measure you can't place on the ground and walk away from.
• I want a brass water bottle if I go travelling to exotic countries.
• Robotic exoskeletons are cool.

Thanks for the subscription mum!

My latest paper

Here's the latest paper I've written, co-authored with Carey!
It's even about MMORPGs in some way (that I don't understand :p ). Check out the links at the very top to write your own.