Question: It never talked about if you wanted to end with a white, or does it do that with the "extend so limit of spaces is 7" thing?
It never talked about if you wanted to end with a white, or does it do that with the "extend so limit of spaces is 7" thing?
You're right that the "doesn't end in white" problem has a lot to do with "extending to 7 spaces"! If you go back to the video at around 1:43, you can see that Professor Loh starts talking about this. He says that using "B" and "WB" blocks can get you a lot of good strings of 6 beads... but there's the slight problem that it doesn't count the ones that end in W!
And that's why we extend it to 7 spaces! Why does this fix the problem? Well, those 7 spaces will always end in black, right? So, the actual "things" we are considering are all those combinations of beads in the first 6 spaces! You can see that the 6th bead could definitely be white, so that solves the issue.
Does that make more sense?
Does this mean that we can flip the WB block around, and make it to become only BW instead, with the combination
\(BWBWBW\), such that it ends in W?