Help needed! Three "rods" pushed one-by-one via one button - how?

This engineering dilemma is making me lose sleep.

Imagine a triangle with a pushable "rod" in each corner.

In the middle is a button that needs to push one of those "rods" and when pushed again, it pushes the next one. Cycle repeats.

Sounds simple right? Well, I can't figure out anything... Ballpoint pencil has similar'ish rotary system but it's quite complex.

Give some ideas, examples, pictures, anything...

SolidworksGeneral