This passcode riddle is an excellent way to introduce factors and multiples and shows the most effective way to understand organized factorization. A good way to understand this problem is by first understanding how a number can be written as all possible products of t natural numbers. Here is a more detailed explanation of how that can be done. Once we have understood this process of writing a number as all possible products of 2 natural numbers, we can move on to understanding how a number can be written as all possible products of 3 natural numbers. For instance, to find the products of 36, a good way to start off would be to write it as 1*1*36. Next, we can break 36 down further and write it using all possible products of 2 numbers. We should get 1*2*18; 1*3*12; 1*4*9; and 1*6*6. We continue this process to find all possible products of 3 natural numbers.

If you enjoyed this problem, here’s another version of a problem with the number 72: "UNSOLVABLE" Logic Puzzle: What Are Their Ages?

You may also visit the educator’s website here to understand factors and multiples in detail. Finally, if you wish to understand more math concepts (who wouldn’t?), visit this link.

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 the control room riddle? - Dennis Shasha

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

Can you solve the temple riddle? - Dennis Shasha

Can you solve the frog riddle? - Derek Abbott

Can you solve the locker riddle? - Lisa Winer

Next Section »