Question 34
Juku has four cans of juice: a $1$-litre can containing $\frac{1}{2}$ litres of juice, a $\frac{1}{2}$-litre can containing $\frac{1}{3}$ litres of juice, a $\frac{1}{3}$-litre can containing $\frac{1}{4}$ litres of juice and a $\frac{1}{4}$-litre can containing $\frac{1}{5}$ litres of juice. There are no volume markings on the cans. Juku wants to measure exactly $\frac{1}{30}$ litres of juice by a sequence of pourings of the juice from one can to another. Letting the juice spill is not allowed. Find out all cans into which Juku can get the desired exact amount of juice.