A candle that burns out completely in one hour costs \(60\) pence, and a candle that lasts for \(11\) minutes is worth \(11\) pence. For some reasons which he doesn’t want to explain to the seller Mr. Fawkes wants to measure \(1\) minute with some of these candles. Can he manage to do that if he has only \(1\) pound and \(50\) pence to spend on the candles?
Mr. Fawkes can only measure the whole interval with each of the candles. He is not guaranteed that any of the candles burns uniformly, so he cannot divide it into two parts. He cannot make it burn faster by igniting them from both ends, but he can extinguish a candle and light it up again later.
There is a 12 litre barrel filled with water, and two empty barrels (one is 5 litres in volume and the other is 8 litres). Using these barrels, try to
a) divide the water into 2 parts with volumes: 3 litres and 9 litres;
b) divide the water into 2 parts with equal volume.
In a parliament with only one house every member had not more than three enemies. Is it possible split this parliament into two separate houses in such a way that each member will have not more than one enemy in the same house as them. We assume that hard feelings among members of parliament are mutual, namely if \(A\) recognises \(B\) as their enemy, then \(B\) also recognises \(A\) as their enemy.
In a scout group among any four participants there is at least one, who knows three other. Prove that there is at least one participant, who knows the rest of the group.