Brain Candy: Gumball Logic for April Fool's Day

Welcome back to Brain Candy! April Fool's Day always lets me down. I fear I am unprankable, mostly because I'm naturally suspicious, but also partly because I have a killer instinct for retaliation. I will get you back. And I will get you back good.

Today's puzzle comes from Mathworld.Wolfram.com:

In 1975, math and science writer Martin Gardner printed this puzzle as an April Fool's joke. He claimed it was impossible to fill in the puzzle using only 4 colors, such that no region shared a border with a region of the same color.

It's possible.

*Beware of the comments, there be spoilers*