Using what we learned here, let’s get back to 2 + 2 = ?.

Believe it or not, you can actually create a Modulo system with any numbers. It does not have to be limited to Modulo 12 like with the clock with the numbers 1 through 12.

Now, our new system is going to be Modulo 3 with the numbers 0, 1, 2. This is a little different from the watch, because a watch doesn’t have 0’s. Let’s quickly refresh what that means.

Modulo 3 with numbers 0, 1, 2 means that after we reach the third number in our set of numbers, we start counting from the first number again. In this case, after we reach 2, we start again with 0. This is just like with the watch, when after we reached 12, we started again with 1.

So now, let’s see what happens when we add 2 + 2 in a Modulo 3, (0,1,2) system.

2 + 2 = 4. But 4 is outside of the numbers that we can use which are 0, 1, 2.

2 is the highest possibility, and we are adding the next two numbers, which are 0 and then 1. Simply put, in this system, 1 represents 4 kind of like 5PM represented 17 o’clock in the watch problem.

In mathematical terms, we now have 2 + 2 = 1.