[The military and some other organizations use a 24-hour clock and speak of "1100 hours" and "1400 hours". But this is still modular arithmetic with 24 replacing 12. For example, four hours after "2100 hours" is "100 hours" (i.e., 1:00 AM the next day). Furthermore, 0 replaces 24 in the military system -- you never hear a military person say "2400 hours".]

We also can do modular arithmetic with numbers other than 12 for the maximum. For example, we can use 5 as the maximum, in which case we call it *mod 5* arithmetic. In mod 5 arithmetic, we use the numbers 0, 1, 2, 3, and 4, and 3 plus 3 is 1, while 2 plus 2 is still 4. If we do arithmetic mod 3, 2 plus 2 is 1, but 1 plus 1 is still 2, etc. You can see the addition tables for a number of different mod numbers by following this link.

One nice thing about modular arithmetic is that there are only a finite number of possible answers. If you assign to each of the possible answers a color, then the triangle can be presented as an array of colored dots or circles. Most of us find it more appealing to look for patterns in this kind of image than in the numbers themselves. The following figures show the first few rows of Pascal's Triangle using mod 3, mod 4, and mod 5 addition, expressed as arrays of colored circles. In these figures red is 0, black is 1, green is 2, blue is 3, and yellow is 4.