Thanks Guest. It is always good to have an answer to compare mine too.
Andrew chooses a number from 1 to 100, and Mary also chooses a number from 1 to 100. (They may choose the same number.) It turns out that the product of their numbers is divisible by 3. In how many ways could Andrew and Mary have chosen their numbers?
Here is the mathematical way.
One or both of them has to choose a multiple of 3. There are 100 numbers and 33 multiples of 3 (for each of them)
There are 33*100 ways for Mary to chose a multiple of 3 and Andrew to chose any number
There are 33*100 ways for Andrew to chose a multiple of 3 and Mary to chose any number
But I have double counted.
There are 33*33 ways that they can both chose a multiple of 3.
So altogether there are 33*100 + 33*100 - 33*33 = 5511 ways. Just as answering guest found.
This could be displayed in a ven diagram. 2 overlapping circles.
33*33= 1089 is the overlapping bits
and 100*33 - 1089 = 2211 in each of the other two arias.