00:01
Hey, stanley.
00:02
So to answer this question, i'm going to start by redrawing the four trees that were posted in this problem.
00:07
I'll begin over here.
00:09
These won't be the pretties, but i'll do my best.
00:21
So right here, you have the first tree.
00:24
Over here, we have the second.
00:38
The third is over here.
00:54
And last but not least, we have number four.
01:11
There we go.
01:12
All right.
01:12
These aren't exactly the cleanest again, but they get the job done.
01:16
So what i like to do in cases of dealing with trees like this is just for the sake of visual clarity, i like to mark each point where there is a branching.
01:27
So places like this or here, here, and here.
01:38
And i find that this just really helps with kind of when you're grouping each of these letters later on.
01:46
Helps you visualize just how to categorize each branching and the members within each branch.
01:55
So next step would be to take a look at this from what i call top down, or basically start from the most recent all the way down to the oldest.
02:08
So in each case, what i will do here is note that the two most recent members, d &e, all branch off from one common ancestor in every single scenario.
02:22
And both d &e are always the most recent instances.
02:26
So to highlight that, what i'm going to do is i'll just draw a circle around each case of d &e just to make it easier to keep that in mind.
02:43
And so what we do from here onwards is we just kind of scale backwards.
02:47
We see, okay, so next point of divergence that the group d and e eventually break off from? what's the other letter that branches off from that same point? and so we see in all cases, that very letter is c in every single case.
03:06
C is what branches off from this next common point that these all share.
03:10
C is also the same here.
03:12
C is the same here.
03:14
And also c is the same here.
03:16
Great.
03:17
Then we move on to the next one where we see that, oh, b is the next diverging pathway from this point where the rest of what we've circled here in green all branch off of.
03:29
And that's the same across every single tree instance here.
03:33
So i'll circle those.
03:36
So all of these now belong to this big sort of green mega group.
03:40
And so we see, okay, what's the last letter that this green megagroup branches off from with a common ancestor? and we see that that is a.
03:52
So having worked our way down this tree from youngest to oldest, we see basically, despite the fact that some of these might be oriented or arranged a bit differently, that there's fundamentally no difference between, say, one, two, three, or four.
04:06
All of these are, as i say, identical.
04:10
There's no fundamental difference between any of these...