This is not a quiz but I am thinking how to write down a simple math formula to count the total number of squares present in a lattice of NxM points for my 12 year old nephew ? He'll sure be happy if I could turn this into, say, a common sense for pupils like him. For example, In a 3x4 lattice there are 20 squares. I first check 3x3 one (by omitting the last column 3x1) on the right and have 12+22+32 = 14 squares then I check 3x3 one (after omitting the first column) on the right to obtain 12+22+32 = 14 squares So there are 28 squares. But I have 2 columns overlapped between the two squares I have just checked. And I have no clue how to reason to leave out the overlapped part to acquire the correct result.