Cleave Books
Puzzle Trio 15

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 my own sort of order, on the 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?

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