You want to prepare a pizza of 12 flavors. You have 12 oddly-shaped pieces of cheese that you decide to use for the pizza. The shapes happen to be ...
Oh, well, forget it! This isn't going to be even remotely realistic. So here is the problem:
I was playing with pentominoes and figured you can pack them nicely in a circle of radius 5.
This immediately cries for the question: Is this optimal? If not, what is the radius of the smallest circle that can accommodate all 12 pentominoes inside without overlap? Show an arrangement that minimizes the radius.
Spoiler alert: the picture above is not optimal.
4.84323 loopy wait
4.86594 Florian F
4.88966 Ravi Fernando
4.92443 Daniel Mathias
4.98189 Przemyslaw Remin Junior