Blame Quintushalls for this.
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Alfik0 wrote: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
i think you're right, thanks! i completely overlooked this.
1 penny on the 1st square, 2 pennies on the 2nd, 4 on 4th, 8 on 8th, 16 on 16th, 32 on 32nd and 64 on 64th gives 1.27$
still, i think it would've been funnier if he had just gone with the arithmetic sequence and given him 20$.
Man, I came to this forum for the first time ever and realized it's not for me based on this thread.
He said one penny on square one, two on square two "and so on". That implies he's putting two on all the other squares as well. It's an English joke, not a math joke and most of you seem to overthink it WAY hard.
$20.80 would've been funnier.
ohgoditburns wrote:Fun fact: there are 69869 different integer sequences beginning with '1, 2' on OEIS.
If this was a XKCD comic that would probably be the comic caption.
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Adkit wrote:Man, I came to this forum for the first time ever and realized it's not for me based on this thread.
Literally one person in this thread has more than one post.
I'm not saying the forum isn't for you. It's probably not. But don't judge the forum based on the assholes in here. We're of a much higher calibre of asshole. Asshole.
It's reference to the wheat and chessboard problem, a classic example in exponential growth and how it surpasses intuition.
https://en.m.wikipedia.org/wiki/Wheat_a ... rd_problem
If it followed that pattern he would receive 18,446,744,073,709,551,615 pennies, or $184,467,440,737,095,516.15.
I did have to come here to find the pattern that made $1.27 though
anonymouscoward wrote:$20.80 would've been funnier.
hagnat wrote: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.
Same same, I was expecting an arithmetic progression and $20.80. Would have been funnier in my opinion.
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OK, I got the joke -- just not quite the joke Zach was actually telling.
I got that the son was expecting $184,467,440,737,095,516.15 (doubling the amount on each square).
Since $1.27 is 2**7-1 cents, I assumed the father just stopped after the
8th 7th square rather than putting 2 cents on each square after the first.
And I thought the "You're lucky it's not $0.96" was a pay equity joke (rather than 1¢, 2¢, 1¢, 2¢, 1¢, 2¢, ...) -- which would have made more sense if the woman had said it rather than the father.
Joke's on you though, Zach -- it was funny anyway!
I guess $1.27 is a way lower figure as compared to $20.80 even if relatively speaking negligible as compared to the exponential 64 squares.
For the $1.27 sequence:
The total value of all pennies on the chessboard is always equal to 2n -1. Hence, on Square1, the total value must be 2(1) - 1 = 1. On Square2, the total value must now be 2(2) - 1 = 3, hence two pennies are added to Square2 to make a total of 3 pennies on the board. On Square 3, the total value must be 2(3) - 1 = 5, so two pennies are put on Square3 to make a total of 5. Thus, 1 penny on Square1, and 2 pennies on all following Squares for a total of 2(64) - 1 = 127.
For the 0.96 sequence:
One penny on every odd numbered square, 2 pennies on every even numbered square, or 1,2,1,2,1,2... for a total of 96.
Moral of the story:
Always request more datapoints!
I suppose it's a bit silly, but you could also get to $1.27 with this sequence: 1¢ + 2¢ + 3¢ + 1¢ + 2¢ + 3¢ + ... + 1¢ (on the 64th square). Basically the same as 1¢ + 2¢ + 2¢ + ... + 2¢.
kst wrote:e "You're lucky it's not $0.96" was a pay equity joke (rather than 1¢, 2¢, 1¢, 2¢, 1¢, 2¢, ...)
Thanks for explaining that bit!
kst wrote:I got that the son was expecting $184,467,440,737,095,516.15 (doubling the amount on each square).
To be honest if the son was expecting that much, and his dad isn't some kind of genie out of a bottle then he's a bit clueless for choosing it. How is dad going to pay up such an amount?
Like many others here I thought his dad was going with an arithmetic progression and came here to see what the actual sequence was.
He should've trained his son in formal logic and game playing. Then again, he probably didn't just so he could pull off this "life lesson".