Another way? (Not the Prof Loh challenge way)
I think I just thought of another way to finish of the question.
Here’s the picture:
@RZ923 I love this photo of your scratch work.. it is so tidy, unlike mine. Prof. Loh always says he likes to do the same problem in many ways, even for a small computational step. It helps you check your answer, and it also helps you to learn little tricks here and there!
In case anyone is wondering how this way compares with the method that Prof. Loh used in the Day 2 Your Turn lesson, the difference is this: @RZ923 is adding the ways in these three sections to get the final total number of ways:
$$ 8100 + 900 + 8100 = 17100 $$
On the other hand, Prof. Loh calculates the ways using Inclusion-Exclusion. In fact, he can be quoted around 0:18 as saying, "Let me first not tell you how much is in this little piece (pointing to the left-side crescent moon shape), where the tens equals the hundreds and the hundreds does not equal the thousands... I will instead calculate the whole piece (the whole circle)."
That's just what he does! He adds the two circles together, and subtracts the overcounted area in the middle.
$$ 9000 + 9000 - 900 = 17100 $$
Yay, we get the same answer! Math is consistent!