How many blocks are needed to build a stair step pattern that has a base of 10, a height of 10, and where each step is one block high and one block deep?

Answer 1

looks like you just want the sum of all the numbers from 1 to 10.

If you list the numbers, you get

1 2 3 4 ... 8 9 10

Now pair them up, starting from the ends. Each pair adds up to 11. There are 10 numbers, so 5 pairs, adding up to 11*5 = 55

Since it looks like you are going to come up against this again, note that if you add up the first n numbers, the sum is

n(n+1)/2