I drew rectangular grids with one more row than their column. The number of dots in the first four grids are 2, 6, 12, and 20, as shown in the diagram below:

What is the total number of dots used in the first eleven grids?

Guest Jan 3, 2020

#1**+2 **

Hello!

We can look for a pattern to count these dots. Note that the 1st grid is 1x2, the second one is 2x3, the third one is 3x4, and so on. This means that the 11th grid is 11*12. Now, we simply have to add these numbers. 2+6+12+20+30+42+56+72+90+110+132. After adding, we get 572, as our answer.

USAMO2019 Jan 4, 2020