## [2016-04-05] college funding

Blame Quintushalls for this.

Moderators: NeatNit, Kimra

foerno
Posts: 16
Joined: Thu Apr 24, 2014 8:35 pm

### [2016-04-05] college funding

http://www.smbc-comics.com/index.php?id=4071

huh? i get the votey sequence (1+2+1+2+...=96) but i'm rocking my brain and i can't figure out how he came up with 127 pennies. the only thing i can think of is if he used a geometrical sequence and stopped at the 7th square for some reason.

2

1+2(64-1)=127.

csostak

### Re: [2016-04-05] college funding

one penny for square 1 and two pennies for the remaining 63.

Ax

1+2+2+...+2=127

gimmetheloot

### Re: [2016-04-05] college funding

On the last two squares of the checkerboard (63rd and 64th), the man gets .63+.64 = \$1.27

csl312

### Re: [2016-04-05] college funding

What I don't understand is under what mathematical system you choose the pennies? Even if you were to place an additional penny for each square on the chessboard (including 2x2, 3x3...8x8) you still only get around \$200. That's where the joke fails to me...

Bruke

### Re: [2016-04-05] college funding

I think the total should be \$2.55 because...

1 penny on the first square (square 1; 1 is equal to 1 squared) = 1 total pennies
2 pennies on square 4 (2 squared = 4) = 3 total pennies
4 pennies on square 9 (3 squared = 9) = 7 total pennies
8 pennies on square 16 (4 squared = 16) = 15 total pennies
16 pennies on square 25 (5 squared = 25) = 31 total pennies
32 pennies on square 36 (6 squared = 36) = 63 total pennies
64 pennies on square 49 (7 squared = 49) = 127 total pennies
128 pennies on square 64 (8 squared = 64) = 255 total pennies

ohgoditburns

### Re: [2016-04-05] college funding

If it's sum 2^n, the number is really really big.

foerno
Posts: 16
Joined: Thu Apr 24, 2014 8:35 pm

### Re: [2016-04-05] college funding

csl312 wrote:What I don't understand is under what mathematical system you choose the pennies? Even if you were to place an additional penny for each square on the chessboard (including 2x2, 3x3...8x8) you still only get around \$200. That's where the joke fails to me...
1+2+4+8+16... =
2^0+2^1+2^2+2^3... =
36893488147419103231

https://www.wolframalpha.com/input/?i=2 ... ...%2B2^64

Keeg

### Re: [2016-04-05] college funding

The joke is in the idea that most things that start with doubling (1 to 2) continue with doubling (2 to 4, 4 to 8, 8 to 16 etc.). In that scenario, you are looking at \$184,467,440,737,095,500.

csl312

### Re: [2016-04-05] college funding

ohgoditburns wrote:If it's sum 2^n, the number is really really big.
I see, I had not thought it is this way. I was thinking the logical continuation would be 3 pennies on the third square, 4 on the fourth... to follow the series 1+2+3+...+64
If it was doubling instead of increasing by one then clearly you would choose the 2^64 pennies. Although you would begin to find a need for a very large chessboard...

ohgoditburns

### Re: [2016-04-05] college funding

Fun fact: there are 69869 different integer sequences beginning with '1, 2' on OEIS.

Idran

### Re: [2016-04-05] college funding

csl312 wrote:
ohgoditburns wrote:If it's sum 2^n, the number is really really big.
I see, I had not thought it is this way. I was thinking the logical continuation would be 3 pennies on the third square, 4 on the fourth... to follow the series 1+2+3+...+64
If it was doubling instead of increasing by one then clearly you would choose the 2^64 pennies. Although you would begin to find a need for a very large chessboard...
It's not just that you'd expect doubling, but that it's referencing a very old, classical math problem.

hagnat

### Re: [2016-04-05] college funding

i was under the impression that the joke would be that he used arithmetic progression, rather than exponential that anyone who knows the chess lore would assume it to be.

Because of that i got my head scrathing on the 1.27 value, instead of 20.80.
As someone pointed out, its 1 for the first position, and 2 for the next 63 positions.
Yeah, despite my best attempts to master english, the language barrier can still be present from time to time.

Alfik0
Posts: 1
Joined: Tue Apr 05, 2016 4:37 pm

### Re: [2016-04-05] college funding

There's one more method to get 127 and I think it's the one meaned(ofc I can't be sure, but...)
You have to double both amount of pennies and number of square, so it will look like it:
square 1 - 1
square 2 - 2
square 3 - 0
square 4 - 4
squares 5 to 7 - 0
square 8 - 8
square 16 - 16
square 32 -32
square 64 - 64
what in total gives 127