Jon's coloured balls solution

Read the puzzle and have a go before reading the solution.

First some notation. Let the six balls be r₁, r₂, w₁, w₂, b₁, b₂.

Denote a weighing by: LHS /\ RHS
where /\ is the pivot.

Denote the weight of ball r₁ by m(r₁) and the others similarly.

Weigh: r₁, w₁ /\ w₂, b₁

What you do next depends on what happens.

1. If the scales balance, then you know m(r₁) = m(w₂) and m(w₁) = m(b₂) basically because the two white balls must be different weights. Swap b₁ for b₂ and see which way the scales tip. This will tell you which of the b's is heavy and the rest follows.

2. If the scales don't balance:

Say they tip to the left; if they tip to the right that is a mirror of what I describe below.

Then you know w₁ must be heavier than w₂, that is m(w₁) > m(w₂) and r₁ can't be light if b₁ is heavy (or they would balance like case 1).
Set them up again as: r₁, b₂ /\ w₁, b₁

Then you have to think carefully through each case:

a. If the scales balance, you know: m(r₂) > m(r₁), m(b₂) > m(b₁) and m(w₁) > m(w₂).

b. If the scales tip left, you know: m(r₁) > m(r₂), m(b₂) > m(b₁) and m(w₁) > m(w₂).

c. If the scales tip right, you know: m(r₁) > m(r₂), m(b₁) > m(b₂) and m(w₁) > m(w₂).