[20160405] college funding

 Posts: 16
 Joined: Thu Apr 24, 2014 8:35 pm
[20160405] college funding
http://www.smbccomics.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.
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.
Re: [20160405] college funding
one penny for square 1 and two pennies for the remaining 63.
Re: [20160405] college funding
On the last two squares of the checkerboard (63rd and 64th), the man gets .63+.64 = $1.27
Re: [20160405] 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...
Re: [20160405] 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
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

 Posts: 16
 Joined: Thu Apr 24, 2014 8:35 pm
Re: [20160405] college funding
1+2+4+8+16... =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...
2^0+2^1+2^2+2^3... =
36893488147419103231
https://www.wolframalpha.com/input/?i=2 ... ...%2B2^64
Re: [20160405] 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.
Re: [20160405] college funding
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+...+64ohgoditburns wrote:If it's sum 2^n, the number is really really big.
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...
Re: [20160405] college funding
Fun fact: there are 69869 different integer sequences beginning with '1, 2' on OEIS.
Re: [20160405] college funding
It's not just that you'd expect doubling, but that it's referencing a very old, classical math problem.csl312 wrote: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+...+64ohgoditburns wrote:If it's sum 2^n, the number is really really big.
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...
Re: [20160405] 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.
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.

 Posts: 1
 Joined: Tue Apr 05, 2016 4:37 pm
Re: [20160405] 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
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