Can You Solve the Locker Riddle?

If you like solving math puzzles, read on.

In this TED-Ed video, we're confronted with the "locker riddle." In it, your wealthy uncle has just passed away, and 100 of his relatives—yourself included—arrive at the reading of his will. Being an eccentric fellow, your uncle's will is bizarre. It stipulates that if all 100 relatives work together to solve the problem (by opening the lockers following a series of rules), you'll share in the inheritance together by unlocking a giant safe, using clues contained in the lockers. But if one person can figure it out without "doing the legwork" (opening the lockers one by one), she will get the entire fortune. You want that full prize!

Watch the video for more details on the challenge, and pause when indicated if you want to puzzle it out for yourself. I'll admit it right now: I was unable to solve this one.

For more on the riddle, check out this TED-Ed page, consult this answer key (PDF download) from a university class, or read this explanation from ProgrammerInterview.com.