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

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*