Matthew suggested I send this in to The Riddler at FiveThirtyEight.com, and to my surprise, they published it!
Four enormous bags of marbles sit in front of you. They are labeled red, green, blue, and mixed.
You want to buy two bags of marbles, but don't want a mixed bag among them. You'll settle for some combination of red, green, or blue. But the shopkeeper alerts you. "Buyer beware," she says, "some jerk has switched around the labels on all the bags, so that now every single bag is incorrectly labeled..."
Kindly, she has allowed you to take marbles out of any of the bags one at a time to inspect what's inside them. "But only two marbles total," she says, "I can't be standing here all day!"
"Or you might lose your marbles," you say to her.
How do you make sure you leave with two bags, neither one mixed, while still only drawing two marbles?
Puzzle inspired by conversations with Jesse Zymet and Adam Greenberg.
Comments
Josh: Thanks to you I was up til 3am thinking about optimal marble picking algorithms and I’m still thinking about it.