As in the Squares and Circles game, here too one is presented with a row of shapes. Each shape is either a square, or a circle, or a triangle. A move consists in selecting any two different shapes. The puzzle has two variants depending on what happens next.

Move with elimination
Two selected shapes are replaced with a single one of the remaining variety. The question here is whether it's always possible to reduce the configuration to a single shape. If so, what shape might it be?

Move without elimination
Two selected shapes are replaced by two shapes of the remaining variety. The question is whether or not it's possible to achieve the configuration with identical shapes only. If yes, what shape might it be?

In both cases, provided the required state is attainable, how do you get there?