00:01
For this question, we're told that we have a chess board as pictured.
00:05
It's not pictured, but we can visualize a chess board with squares numbered 1 through 64.
00:10
You have a huge change yard with unlimited number dimes.
00:14
And on the first square, you're going to put one dime.
00:16
Okay.
00:18
So we just kind of visualize a chess board here.
00:21
Right.
00:21
So on the first square, we're going to put one dime.
00:24
On the second, we're going to put two times.
00:27
And then we're going to keep doubling, right? so then four and then eight and then 16, two, three, four, five, six, seven, eight, and so on.
00:43
Right.
00:43
So 16, 32, and so on.
00:47
So we can see that these are just doubling.
00:48
So these have to do with powers of two, right? so here's two to the first.
00:56
This is two squared, two cubed.
00:59
So does a pattern fit backwards? is this two to zero? yep, sure enough, this is two to the zero power, right? so it looks like my general pattern here is for the first square, for the first square, it was two to the zero.
01:13
For the second square, it was two to the first.
01:16
For the third square, it was two squared.
01:19
So it looks like for the nth square, it's going to be two to the n minus one.
01:28
And so here are some questions it asked.
01:30
This is how many times we have stacked on the seventh square? so on the seventh square, this should be 2 to the 7 minus 1, which is 2 to the 6th, which is 64 dimes.
01:41
I said 64 and wrote 24.
01:43
How about that? 64 dimes.
01:47
Okay, 64.
01:49
And then it says how many dimes will be stacked on the nth square? well, we already answered that right here.
01:54
On the nth square will be 2 to the n minus 1.
01:59
So the minus 1 is up in the exponent.
02:01
So let me rewrite this here because one's kind of dragging down.
02:04
So 2 to the n minus 1.
02:07
So the n minus 1 is the minus 1 is in the exponent...