Re: Mathematical function for Smiling Jack the Anarch

bwross wrote:
On Sep 28, 9:56 pm, devilwithcape
<devil_in_the_pale_moon_li...@xxxxxxxxx> wrote:
The function is:

f(x) = x[ (x+1)/2 ]

where x equals the counters on Jack.

Yep, that's the sum of integers from 1 to x. The sequence is also
referred to as triangular numbers, because they count the number of
items arranged as a triangle
like this:

* * * *
* * * * * *
* * * * * *
* * * *

It's a very useful sequence and function to know. It comes up a lot
in math as well as in games.


There's a story where Carl Friedrich Guass (a famous mathematician in
the first half of the 1800s) was made to calculate the sum of the
integers from 1 to 100 as a punishment as a school kid. What he did
was consider:

1 + 2 + 3 + ... + 100

and he added

100 + 99 + 97 + ... + 1

to it (meaning that he was calculating twice the wanted sum, but you
can always just divide by two afterwards).

Now notice that if you add the nth number from the first sum and the
nth number from the second, it always adds up to 101... for 100 times
total.

So he had, 2 * f(100) = 100 * 101.
Divide through by two and you get f(100) = (100 * 101) / 2 = 50 * 101
= 5050.

Or in general, the function you have.

Brent Ross

So are you saying, if I let SJ stand around for 100 turns, I'll lose 5050? Or, burn Jack ASAP as he hits the table...?

best -

chris
.

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