My casework method...
Ok, I admit I didn't do the only-top-row method like Prof Loh did, but I did a similar method:
Like him, I discovered that horizontal 1x3's come in 'clusters', meaning that I can see them as one group.
My casework was based on the # of vertical rectangles:
- If there're 0 vertical's, then there are 3 'clusters' - 1 way
- If there's 1 vertical...wait, that's not possible! You can't fit 3's into 8! - 0 ways
So the number of vertical's must be a multiple of 3...
- 3 vertical's, 2 clusters - 10 ways
- 6 vertical's, 1 cluster - 7 ways
- 9 vertical's, 0 clusters - 1 way
Total = 19 ways
@rz923 This is really nice! I've also linked this to the Your Turn Part 3 lesson.