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Topic: Combination\Permutation with Average Constraint Question
Replies: 2   Last Post: Aug 13, 2008 9:49 AM

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Idgarad

Posts: 20
Registered: 10/18/06
Combination\Permutation with Average Constraint Question
Posted: Aug 12, 2008 1:21 PM
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I am working on a collectable card game as a hobby. I want a
definitive set of cards that I can plan on crafting by allocating 0 to
100 points to spend on creating the card in any 8 areas.

Given 8 possible attributes to each card, ranging from 0 to 100 how
many possible combinations are possible to get:

-=> an average of 25 (common cards)
-=> an average of 50 (uncommon cards)
-=> and average of 75 (rare)
(or from a purely formula base; How can I get the possible
combinations of X atrributes ranging from L to H such that the average
is exactly Y; given L,H,X, and Y are whole numbers.)

The idea is that I have laid out a point system to creating a card
giving a card designer (my friends) either 200, 400, or 600 points to
build a card to ensure a basic balancing system in their creation.

How many cards are we looking at creating?

I know it's a huge number, but how huge?

Not an easy task I am finding...

from a function standpoint I suppose I could try a brute force check
of
function(a,b,c,d,e,f,g,h)
if average(a,b,c,d,e,f,g,h) == 25 return 25;
if average(a,b,c,d,e,f,g,h) == 50 return 50;
if average(a,b,c,d,e,f,g,h) == 75 return 75;


and then walk a-h incrementing them from 0-100 recursively...

Any good mathmatics to work around a brute force approach?



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