I need to design build and test a device that'll keep an ice cube from melting for 3 minutes in boiling water

a larger ice cube?

you need a well insulated container so the heat of the water does not penetrate the insulation and melt the ice. Insulate and you will succeed!

its already been invented ,NASA uses it.they call it frozen smoke.

Styrofoam is an excellent insulator and very easy to work with. Wrap it in plastic wrap to make it water proof. I bought a Styrofoam cooler from 711 for $2.99 and put ice and beverage in it. I left it in the very hot car over night and the next day and the next afternoon hardly any ice had melted and the beverage was just icy cold. The insulative value wouks the other way with heat too. Good Luck

use salt it changes the freeing point so while the ice melts the temper ture gets cooler

3 minutes is not very long, a simple plastic pill bottle might do it, depending on whether "melting" means completely, or "at all". If the requirement is to not melt at all, then you will need to start with ice colder than the freezing point (most freezers are colder, but don't let the ice sit around tool long before doing the experiment) if you can soak the ice in liquid nitrogen before starting that would be a plus, but probably not allowed. You will also need good insulation, expanded polystyrene (EPS)" beadboard" is pretty good, extruded polystyrene foam (XEPS) , one trademark is Styrofoam™, might be slightly better if you can find it.