Prize Puzzle Competition 15

Closing date is 26th February 1999

43. Traffic lights are a familiar sight with their distinctive red, amber and green being shown in a regular order, delivering 4 different messages to motorists.
However, they could be used to deliver more messages than that.

Assuming each message requires at least one light to be showing - how many different messages would be possible?
traffic lights

44. Line of books I recently bought a 10-volume set of encyclopaedias.
At present I have only arranged the first 9 volumes in order on my shelf, as shown on the left.

Using my system, where should Volume 10 go?

45. On a piece of ground (which is flat and level) there are two vertical flag-poles.
One is 7 metres tall and the other is 5 metres tall.
Each has a stay-wire running from its top to the foot of the other.

What is the height above the ground of the crossing-point of the two stay-wires?

The winner of Competition #14 was Peter Murdoch of Leeds
The answers were:

41.70 different ways.
42. 13 dolls were needed
The number of entries was very low. We suppose this to be an indication of how busy everyone was at that time of year, and hope that the New Year will see the return of our many "regulars".
Make a New Year resolution: "I must do the Competition regularly"!
Happy New Year for 1999 anyway.