Thursday, 4 June 2009

Compound parabolics

How can you design a parabola which can focus sunlight at the focus at different time of the day without tracking?

Here is the answer:

And a mould for creating the compound parabolic solar cookers

What's you call?

Today on Australian Seven's "Deal or No deal", it is a classic probability case.

In the last round, the contestant was left with his and his daughter's cases to open. The board has $4000 and 50cents. The host has been playing up for a mega-guess which would be $10,000. The bank offers $2020, should he accept it? (Answer in white below. Highlight to cheat and see my answer.)
No. We can do much better than that.
In the show, he did not accept the offer and has chosen "no deal". As expected, the mega-guess was offered. What should be the guess by his daughter?

She should have guessed that she has $4000. If she is right, they combined would have $10,000.50. If she is wrong, her father would have $4000. In both cases, it would be better than the bank's $2020 offer. However, they did not play the game optimally. The game ended with 50cents for both of them.