# Thread: Solve for X where sum of x's with consecutive exponents equals 1

1. ## Re: Solve for X where sum of x's with consecutive exponents equals 1

Thanks. To Debsta, '**' means 'to the power of', at least it did way back when I was in high school. So, 5**2 means 5 to the power of 2, or squared.

To Plato, that is certainly a way to fully distribute the money, but it doesn't halve each payout as you move from 1st to 5th place.

Getting back to Debsta's example, if the prize money is 62, then the payouts would be: 32, 16, 8, 4, 2. Each successive payout is half of the previous and all of the prize money is awarded.

2. ## Re: Solve for X where sum of x's with consecutive exponents equals 1 Originally Posted by sumdumgai Getting back to Debsta's example, if the prize money is 62, then the payouts would be: 32, 16, 8, 4, 2. Each successive payout is half of the previous and all of the prize money is awarded.
Did you see my post?

3. ## Re: Solve for X where sum of x's with consecutive exponents equals 1

Thanks DenisB. No, I am not fooling around. 121.29 is the correct payout for 1st place if all of the payouts are to equal 235. Divide 121.29 by 2 to get 2nd place, divide that result by 2 to get 3rd place, and so on. The last place payout would be 7.58.

4. ## Re: Solve for X where sum of x's with consecutive exponents equals 1

DenisB. You've solved my problem and you get 1st place prize, 121.29 thank you's. I got 121.29 using a different method (Excel VBA programming), but yours is better.

5. ## Re: Solve for X where sum of x's with consecutive exponents equals 1

Here's the expression that I will use to compute the payout for each place:
(2^(numPlayers-1)*prizeMoney/(2^(numPlayers)-1))/2^(place-1)

^ is exponent sign

6. ## Re: Solve for X where sum of x's with consecutive exponents equals 1 Originally Posted by sumdumgai DenisB. You've solved my problem and you get 1st place prize, 121.29
US funds?

7. ## Re: Solve for X where sum of x's with consecutive exponents equals 1 Originally Posted by sumdumgai I have a problem where I have to distribute some prize money, halving the prize money each time until every participant receives their share and no money is left.
For example, first place gets half the prize money. Second place gets half of what's left, etc. Last place gets remainder which was double the money given to the next to last place participant.
Once more, that's very badly worded; should be:
1st place gets a certain amount, 2nd place gets half of what 1st place got,
and similarly until last place gets half of what the previous participant got.

Btw, that turns out to be a "geometric series",
the multiplier being 2 if you start with last place,
or 1/2 if you start with 1st place.

If you wanna learn more, google "introduction to geometric series".