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**Riddle 1**

30 Prisoners are on death-row for marijuana related offences. The prison warder doesn't view their crimes with much seriousness,and decides to give them a chance to escape.He makes the prisoners the following offer:

Tomorrow all the prisoners will be blindfolded, and either a black or a white hat wil be placed on their heads. All the prisoners will then be placed in a row, all facing the same direction in line with the row (so all but one is facing someone elses back). Then their blindfolds will be removed. They cannot see their own hat, or those on the people behind them. But they can see all the hats of the people in front of them.

The deal is that the prisoners themselves get to guess what colour hat they are wearing. If they guess correctly, they will be freed. Otherwise not. Thus the prisoners are faced with finding some strategy to maximise the number of prisoners that will be freed. What is this strategy, and how many prisoners will be garuanteed their freedom? And how many prisoners will be freed using it?

**Riddle 2**

Suppose there are 17 scientists. Each scientists corresponds (writes letters etc.) with each other scientist, and they correspond about only 3topics, and any two scientists correspond about exactly one topic with each other. Show that there exists at least three scientists who correspond with each other about the same topic.