## Help solving very difficult math puzzle

For the discussion of math. Duh.

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DEZ1389
Posts: 3
Joined: Thu Feb 11, 2016 5:28 pm UTC

### Help solving very difficult math puzzle

Hi there,

I sincerely hope you can help me. I hope to find the max value of this mathematical thing. Ready? Here it comes.

There are two sets (jungle population for example).

The jungle has many different categories animals in it. Say A,B,C,D,E,etc.
An animal can be present or not
Furthermore, the quantity of every animal can range from 1--->infinite
So, to put it together: jungle 1 can have X categories of animals, where every category can have 0 to X of the same animal.

The second jungle (Jungle 2) has the same conditions.

I want to know the minimum and the maximum value if I put the two jungles together.

The values are calculated according to a fomula that exist of two formulas/parts (That INTERACT)

1. Overlap
Based on the formula
O= the sum of the minimum of each proportion of the category's total to the total.
So say there is the category of lions
In jungle 1 there are 1000 lions and in total 10,000 animals =0.1
In jungle 2 there are 500 lions and in total 4,000 animals = 0.125
Then the minimum of that category is 0.1
This should be done for all categories (the max for this formula is obviously 1 when there is a full proportional match)

2. Proportional increase
For this formula I first need to calculate for jungle 1 (pre-merged) the sum of the squared (categories total/total total)
So say there are 1000 lions and 9000 tigers
(1000/10000)^2 + (9000/10000)^2
So say 500 lions, 2000 zebras and 1500 rhino's
Then I calculate again for the merged jungle
(1500/14000)^2+(9000/14000)^2+(2000/14000)^2+(1500/14000)^2
Finally I take the absolute change between the merged and the pre-merged jungle (this ranges from -1 to 1)

3.
Values are calculated according to the following formula

e^overlap x e^proportional increase

I already know the minimum value:
No overlap, proportional increase = -1, so Value is e^-1
But what is the maximum value. I don't have a clue, but I really want to know.
Could you solve this question?

DEZ1389
Posts: 3
Joined: Thu Feb 11, 2016 5:28 pm UTC

### Re: Help solving very difficult math puzzle

Anyone?

Carlington
Posts: 1588
Joined: Sun Mar 22, 2009 8:46 am UTC
Location: Sydney, Australia.

### Re: Help solving very difficult math puzzle

If the maximum is 1 for formulae 1 and 2, shouldn't the maximum for 3 be e^1 × e^1 = e^2?
Unless there's something I'm missing, or some reason that overlap and proportional increase can't both be 1?
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DEZ1389
Posts: 3
Joined: Thu Feb 11, 2016 5:28 pm UTC

### Re: Help solving very difficult math puzzle

Carlington wrote:If the maximum is 1 for formulae 1 and 2, shouldn't the maximum for 3 be e^1 × e^1 = e^2?
Unless there's something I'm missing, or some reason that overlap and proportional increase can't both be 1?

Hi
No max can't be e^2
If there's a full overlap there is no increase in the concentration of the population.
Therefore, for a full overlap the outcome is E^1 = 2.72
In contrast, if there is an increase in concentration of 1, there should be 0 overlap (otherwise concentration can't increase by approx 1).
Therefore, max for this situation is also E^1

However a diversified jungle relatively inhabited by one category and a jungle fully inhabited by the same category, could for instance lead to an overlap of 0.759 and a concentration increase of 0.285 = 2.85

Therefore, I think mathlab is needed to find out the maximum.