How to Solve the Problem of Accommodating New Dragons of Both Ice and Fire Into an Existing Kingdom

Ted-Ed presents “The Riddle of Ice and Fire”, written by math educator Henri Picciotto and animated by Igor Coric of Artrake Studio, where narrator Addison Anderson poses the question of how to accommodate the arrival of five new dragons, some requiring ice and some requiring fire, into a land where elder dragons of different preferences live in complete harmony.

It’s your first day as Center Realm’s official cartographer, and you’ve already got a big problem. Center Realm is home to three elder dragons: two ice, one fire, and they’ve lived in harmony for centuries. But scouts have sighted three fire dragons and five ice dragons flying towards the region. Can you figure out where to place the new dragons?

The answer lies in how to best draw a map in order to keep the fire dragons separate from the ice dragons, and vice versa.

The pattern is that points where lines meet must be surrounded by an even number of regions. So what we want to do is connect those to each other. Each line adds a single new region that touches both meeting points. There are several ways to do this to accommodate all 8 new dragons.