Hard Question!

[johny321]

Guarantee no one will solve it!

 

 

 

Consider two breeding strategies of the fictional Furble. Dominator Furbles can fight for a breeding territory, and if they win, will be able to rear 10 offspring. An alternative is to share territory with another Furble which will allow each to rear 5 offspring. Sharers who attempt to share with dominators will be forced out of the territory, although they will be able to find a new territory. Assume sharers become extra cautious after encountering a dominator and so will always find another territory to share the next time around, but due to lost time will only be able to produce 3 offspring. Dominators are always able to force sharers out of the territory and rear 10 young. Dominators who meet dominators will win 50% of the time. When they lose, they are not able to reproduce that season due to sustained injuries. Individual Furbles cannot switch strategies.

 

With a total population of 2000 dominator and sharer Furbles, how many would you expect to be dominators?

[atinymonkey]

Guarantee no one will solve it!

 

The http://www.highiqsociety.com has asked that this question not be answered on forums. It negates it as an online test for applicants.

 

If you are really stuck, go to http://www.furbles.co.uk/ and use the software to create a population.

[johny321]

Ok!

[gnpatterson]

Without answering the question I will discuss how to solve it.

 

the main issue in these quesitions is to form a self consistency equation with the various population types across a number of generations if necessary.

 

Then solve the equations. you need to form the equations across enough generations to include all the historicity of the system.

 

The creatures in the question are two distinct populations but the problem I have is in parsing the information given and in getting to grips with exactly what the sequence of events is.

 

there does not appear to be any restriction on the territory so the solution is one in which a stable proportion of the two populations are exploding exponentially

 

The life span of the creatures seems to be infinite which helps get rid of complexity

 

The issue that I am stuck on is deciding on the factors that influence the interaction of the two populations, I suppose i have to assume some sort of territorial lottery with all creatures getting an equal "A priori" chance (this excepts the displaced sharers)

 

As far as the dynamic stability of the system is concerned it seems to me that the system is likely to be stable as sharers have their "get out of jail free card" and effectively expand "ahead" of the dominators.

 

the spacial distibution of the individuals is of course not relevant.

[gnpatterson]

Ha Ha furbles.co.uk is of course a red herring

 

If you want to research the question "population dynamics equations" should form a useful google search

[johny321]

By the way, does this High IQ Society pay your salary? So, does it really matter to our lives if we reveal a few answers. Also, you could only have an IQ of 96 and still get in by repeating the Tests over and Over again.

[atinymonkey]

By the way, does this High IQ Society pay your salary?

No.

 

So, does it really matter to our lives if we reveal a few answers.

Well, yes. It matters for a few reasons: -

 

1) You have presented the copyrighted property of a company that has expressly asked that the answer not be given. It would be polite to respect that wish.

 

2) If the answer is given, then the Admins may get a request to delete the thread from the institute when the thread propagates.

 

3) Providing the answer will undermine the effectiveness of the test for people who google for answers during quizzes.

 

4) Because the question is copyrighted material, posting it without the thread citing reference is in breach of the forum rules. My post showing the source protects the site.

 

Also, you could only have an IQ of 96 and still get in by repeating the Tests over and Over again.

I have no idea. It's possible, I suppose. It's not my request, you would have to take it up with the International High IQ society. I'm guessing it's a preventative measure rather than an infallible system.

 

I don't really mind either way, I'm just mentioning it.

[johny321]

By posting the results I'm actually helping the organization. As long as there are people who know the answers, they are able to just go and do the tests without hinderence from long, hard questions.Therefore, having straight access to membership

[atinymonkey]

I'm ringing the Royal Society for Prevention of Cruelty to Logic.

[gnpatterson]

why would you want to cheat? why would you want to be a member of a highQ society (at all)? if you are not smart enough to solve a problem your self why would you want to join a society that would just give you more problems that you could not solve yourself.

 

I have to agree with atinymonkey, the puzzles are copyright and property of the site.

Just giving the answer would spoil the puzzle for any one wanting to do it for real.

 

HOWEVER

 

Some of the puzzles are of dubious provenance. The 24 squares is a published discovery of a group of mathematians. The Doughnut problem also published.

 

The standard of puzzle is hardly going to separate out the "highly gifted", they are merely a pasttime that some rather egotistical and stupid people are going to use to impress themselves with.

 

Groucho Marx: "I don't want to belong to any club that will accept me as a member"

[johny321]

Well, believe it, there is a large cash prize up for grabs to any one who answers all 25 correctly. So, it can be said it's worth a shot!

[gnpatterson]

the debate is "pie in sky" vs "sour grapes"

 

the trick is to know ahead of time if you are the fox or the crow.

 

I really think it is only worth doing if you are going to get enough out of the effort to make it worthwhile in any case.

[atinymonkey]

Well, believe it, there is a large cash prize up for grabs to any one who answers all 25 correctly. So, it can be said it's worth a shot!

Good luck with that. I'm sure it's a winning idea.

[johny321]

Well, if we are going to use an exponential equation we need to know the original population, and how do we find it from the given info?

[gnpatterson]

No you dont use an exponential equation, you use the assumption that each generation is the same make up as the previous

 

the equations you make are for the probabilities that certain things will happen

 

the probability that some thing will happen is based on the population distribution and the population distribution is based on the probability that certain things will happen.

 

then you use a self consistency arguement

 

In some ways i like these type of problems in other ways i hate them

 

they work on the basis that you can solve them if you assume you can solve them on the other hand it requires more confidence than I normally have.

[johny321]

So, its prety much an answer like Furble Population= (1/2)^2 + (1/8)/ .02323 + ( k-1)

Even though thats not the answer, it's some thing like that

[gnpatterson]

well start by writing out the information given as statements that invlove the probability of it happening

 

for example

 

New dominators = 10 * (prob that dominator will win * prob that dominator meets dominator + prob that dominator meets sharer) Old Dominators

 

New sharers = 5 * prob sharer meets sharer * Number non-cautious sharers

_____________ + 3 * Number of cautious shares

 

NB there is a flaw in one or both of these equations but I'm not giving the answers away for free any more.

[johny321]

I was told game theory would solve it,

 

# S D

S 5 3

 

D 10 5

[PhDP]

why would you want to be a member of a highQ society (at all)?

 

Why somebody would want to be in a HighIQ society anyway ?

 

And gnpatterson, maybe it's because I partyied a lot, but your explanations make my head hurt a lot, it isn't that complicated...

[gnpatterson]

which problem is not that complicated?

 

a) the inexplicable motives of people or

b) the proportion of furbles

c) both

d) none of the above

[gnpatterson]

the only game theory I know is the min-max theorem. but to get to that point you have to do a lot of probability work, this question seems to have a lot of probability work, but i'm not sure that qualifies it to be called game theory.

 

usually in game theory you are asked to optimise a strategy, in this case you are not allowed to change the strategy. I can see the similarity in the situations but not how game theory applies, except of course that the proportion of furbles is going to stationary at some optimal growth rate.

 

I can see the matrix you have drawn and I would suppose that it should/could be decombosed into eigen vectors for the stable and unstable proportions.

 

this would give you a couple of answers to use as guesses and the site would let you know which one is the correct one.

[gnpatterson]

Also from your matrix I can see that the assumption I was making was that sharers that got kicked off their territory don't bred that year but do bred next year is wrong and that I was making it too complicated. However surely the matrix should include the information about the number of surviving furbles ie a +1 to each term?

[gnpatterson]

got it!

 

it _was_ so much easier to do than I was making it!! so much for the question being for exceptionally gifted, if I had just read the question carefully to start with. I suppose all i have to do is enter two sets of answers in to the site, one deliberately wrong and one with my guess.

[john321]

How????? What method do you use?

[atinymonkey]

got it!

 

it _was_ so much easier to do than I was making it!! so much for the question being for exceptionally gifted' date=' if I had just read the question carefully to start with. I suppose all i have to do is enter two sets of answers in to the site, one deliberately wrong and one with my guess.

[/quote']

Well, I was wondering if my answer was too simplistic after seeing your workings! But I think you are right, it's meant to be answered on the fly. It's a logic question more than a mathematical one.