**Which is Which**.

You have ten balls - five red and five black, having precisely the same shape and size. All the red balls weigh differently, i.e. one of them is

*very heavy*, the other

*heavy*, another is

*medium*, another is

*light*and the fifth

*very light*. Each red ball has a black twin of the same weight. It is known that:

(i) A

*very heavy*and a

*medium ball*put together weigh as much as two

*heavy balls*.

(ii) A

*heavy*and a

*light ball*put together weigh as much as two

*medium balls*and:

(iii) A

*medium*and a

*very light ball*put together weigh as much as two

*light balls*.

Determine the least number of weighings required on a balancing scale to determine which is which, given that:

(i) Each ball can only be paired with a ball of like color before weighing, but pairing a given ball with its twin is not allowed.

(ii) Each ball can also be paired with its twin (in addition to a ball of like color) before weighing.