Problem 20: Measure for Measure

In each of these two famous problems you must measure certain quantities in creative ways.

1. You have two pieces of string, both of which take exactly one minute to burn. However. they do not burn evenly – at some points they burn faster and at others slower. Using the two strings, how can you measure exactly 45 seconds?
2. You have three jugs with volumes 8, 5 and 3 litres respectively. The 8-litre jug is full and the 5-litre and 3-litre jugs are empty. How can you pour the water between the jugs in such a way that the 8-litre and 5-litre jugs each end up containing 4 litres of water, with the 3-litre jug empty? You cannot use any measuring equipment, and the jugs are all weirdly shaped (so for example you can’t accurately pour out half of the water in a jug by eye).