The locker problem is often used as an introduction to factors, multiples, square numbers, prime numbers, and sequences. It shows that some problems can be solved using a smaller, simpler problem rather than brute force (also known as the method of exhaustion). Here is a more detailed video solution to the locker problem, and here is a related problem that uses Othello pieces instead of lockers.

If you enjoyed the locker problem, you might enjoy studying figurate numbers. Another fun problem to investigate is the handshake problem. An interesting extension is to write square numbers as the sum of odds. Visit the educator's blog that links these units together, and another that is from the viewpoint of students who learned about it.

Love riddles? TED-Ed has plenty of them that will challenge you:

The famously difficult green-eyed logic puzzle - Alex Gendler

Can you solve the prisoner hat riddle? - Alex Gendler

Can you solve "Einstein’s Riddle"? - Dan Van der Vieren

Can you solve the temple riddle? - Dennis E. Shasha

Can you solve the frog riddle? - Derek Abbott