How many squares?

I keep seeing this puzzle on Facebook, so I'm posting my systematic solution here.



There's a pattern of 16 basic squares in a regular 4  x  4 grid, plus two more superimposed on that grid to create 8 small squares.

First consider the basic squares.  There are 4 x 4 = 16 of them.

Now group them into 2 x 2 squares. There are 3 of those across:



and there are obviously 3 of them down also, so there are 3 x 3 = 9 of them.

If you do the same using 3 x 3 squares, there are 2 across and 2 down, so there are 2 x 2 = 4 of them.

And of course if you group them into a 4 x 4 square, there's just 1 of those.

Now if you do the same with the two superimposed squares, there are 8 small squares and 2 large squares:



So the total number of squares is:

16 + 9 + 4 + 1 + 8 + 2 = 40

Your life in 5-year snapshots

Here's something new: describe your life on a single page by writing single-sentence snapshots of your life at 5-year intervals. Here's my one-page history:

5 years ago: Teaching math, science and information technology at an independent school in British Columbia.

10 years ago: Independent consultant doing functional specification documents for industrial software development projects in Georgia (US).

15 years ago: Staff consultant at software company in Seattle, applying their products to customers' needs and designing software to fill any gaps.

20 years ago: Selecting computers, designing networks and implementing process management software at large new pulp mills in northern Alberta.

25 years ago: Teaching computers, electronics and logic to engineering technologists at a new division of a college in Surrey, British Columbia.

30 years ago: Developing software to automate the startup of a process plant in British Columbia.

35 years ago: Overseas resident control systems engineer for a project to design and build a large pulp and paper mill in Poland.

40 years ago: Owner/operator of an business doing recording, editing, and duplication of radio programs and educational material in Vancouver, BC.

45 years ago: University student and anti-apartheid activist in Durban, South Africa.

50 years ago: At boarding school in Lusaka, Zambia completing A-level university entrance requirements in math and science.

55 years ago: Completing elementary school and editing the class annual.

60 years ago: Leaving the UK and flying to my new home in Northern Rhodesia.

65 years ago: Learning to hate the daily spoonful of cod liver oil all British kids got from the National Health System!