You have six balls - three red and three black. All the red balls weigh differently, i.e. one of them is heavy, the other medium, and the third light. Each red ball has a black twin of the same weight. A heavy and a light ball put together weigh as much as two medium balls.

What is the least number of weighings required on a balancing scale to determine which is which?

I think you can do it in three weighings.

124 against 356

125 against 346

25 against 14

note: red balls are numbers 1,2 and 3

I also have poss second weighing 154 / 326 but third weighing would need modifying.

Depending on results one has to reason pairings and weights.

I'm checking it through but even if not right I believe there is a three weigh solution based on one of these two first and second weighings. The reasoning is a little difficult but possible.

Anyway it's a line of attack if anyone can modify it or prove/disprove it I'd be grateful