Pascal’s Triangle is an isoceles triangle that is created by starting with the number 1. This 1 at the top makes up Row 0. The first row (1 & 1) contains two 1′s, both formed by adding the two numbers above them to the left and the right, in this case 1 and 0 (all numbers outside the Triangle are 0′s). Do the same to create the 2nd row: 0+1=1; 1+1=2; 1+0=1. And the third: 0+1=1; 1+2=3; 2+1=3; 1+0=1. In this way, the rows of the triangle go on forever.

There are many uses of Pascal’s Triangle. For example:

• The sum of the numbers in any row is equal to 2 to the n^th power or 2ⁿ, when n is the number of the row. For example:

• If the 1^st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1′s) are divisible by it. For example, in row 7 (1 7 21 35 35 21 7 1) 7, 21, and 35 are all divisible by 7.

• The triangular numbers can be found in the diagonal starting at row 3 as shown in the diagram. The first triangular number is 1, the second is 3, the third is 6, the fourth is 10, and so on.