Student Lockers & Math

The purpose of this activity is to provide insight into the math behind a student’s locker. The main topic covered is that of permutations, however, we will refer to it as combination since this is what students refer to it as). Even if your students are not ready for permutations they will find the activity interesting and it may serve as a great introduction to other math topics.


Imagine that you wanted to steal a diary out of your best friend’s locker to see what she was writing about you. You don’t know her locker combination but you plan on guessing three times a day until you get in. Will you eventually get into it by the end of this school year?

Let’s assume her lock has 40 digits and her actual combination (PERMUTATION!) is 3 digits. Take a guess how many different possible combinations there are? Next, calculate how many guesses you will be able to make at three times per day within a school year (180 days x 3 = 540 guesses).


The actual number of possible combinations (PERMUTATION!) calculated is 64,000.


With this number in mind, calculate how many days you would need to ensure you guessed the right combination (64,000/3) =21,334 days)?



What percentage chance pre year is this (540/64,000= 0.8%)?

The math behind the number?

The following is know as a Permutation with repetitive numbers allowed



Each digit has a 1/40 chance of being correct. Thus, with a 3 digit combination possibilities are calculated as



40 x 40 x 40 = 64,000

Activity Sheet:

1) Will you eventually get in to her locker by guessing three times a day? _____



2) How many possible combinations there are?



3) How many guesses will you make at three per day for a school year?



4) Based on this, with 540 guesses what percentage of chance do you have at guessing the right combination? ______%



5) Given the actual number of combinations, how many days would you need to ensure you guessed the right combination?________How many school years is this_______?



6) What is your actual percentage chance of guessing the right combination in a school year? ___________