00:02
Okay, i've got a chess board with 64 squares, and on the first square i put one dime, and on the second i put two dimes.
00:14
So i'm going to start a table here.
00:17
Let's do square, number, and number of dimes.
00:28
Okay, so first square i put one dime, second square i put two dimes, and i continue always doubling the number.
00:40
So on the third square i'm going to double two to get four, fourth square i'm going to double it again, fifth square, double it again.
00:55
And then hopefully you start to notice that these numbers that i'm writing for the number of dimes are all powers of two.
01:04
One, two, four, eight, sixteen, thirty -two.
01:12
So, i'm going to be doing this a lot, up to 64 squares, so i might want to think about a formula.
01:23
Like, for instance, the second square is two to the one, and the third square is two to the two, two squared is four.
01:35
Two to the three is eight, two to the four is sixteen.
01:42
What about that first square? well, that's going to be two to the zero, because anything to the zero power is one.
01:51
So, if i call my square n, then what's my formula going to be? it's not going to be two to the n, because i notice, like, this is square six, but this is five.
02:11
This is square five, but this power is four.
02:14
This is square four, but this power is three.
02:17
The power is always one less than the square number.
02:21
So, this is actually two to the n minus one.
02:28
Okay, so now part a says how many dimes will you have on the tenth square? so, on the tenth square, my formula is going to be two to the ten minus one, which is two to the ninth.
02:51
And i'll use my calculator to figure that out.
02:56
Two to the ninth is going to be pretty big.
02:58
It's going to be 512.
03:04
Okay, so maybe i could have figured that out by just continuing to double.
03:09
32 double is 64, then 128, then 512.
03:21
Let me do it that way as well.
03:29
So, 7, we're going to double to 64.
03:34
Eighth square, 128.
03:42
Ninth square, 512.
03:52
Why do i feel like i'm off by one? because i'm off by one because 128 times two is 256.
04:05
Just jumping the gun on my powers of two.
04:12
And then double that, 512.
04:16
So, we could have done it that way as well.
04:19
Okay, that was part a.
04:22
Part b says how many dimes will you have stacked on the nth square? okay, well that's this part here.
04:33
We're going to have two to the n minus one.
04:36
On the nth square, i'm going to have 512 on the ninth square.
04:44
Part c says how many dimes will you have on the 64th square? okay, so this was part a.
04:55
This was part b.
04:59
Part c, we're going to have two to the 64 minus one, which is two to the 63.
05:10
Let's see.
05:12
Two to the 63 with the calculator gives me a very big number.
05:18
We get 9 .22 times 10 to the 18th power.
05:29
And part d says, assuming a dime is one millimeter thick, how high will the last pile be? okay, so it's going to be 9 .22 times 10 to the 18th millimeters...