Puzzles for Traders

[Seeker 11]

I thought that I would post a series of coffee-break puzzles, partly because they're fun, but also because they can lead to a better understanding of the statistical processes that underlie the assumptions we often make when evaluating trading approaches . . .

 

A city has a large hospital and a small hospital. Each has a maternity ward. Yesterday, 60% of the births at one of these hospitals were boys.

 

Which hospital is this more likely to be?

 

BlueHorseshoe

 

The conclusion that it is the small hospital is incorrect. We simply don't know. The argument that it is determined by the sample size, doesn't hold weight, since we don't know what the sample size is for either. One hospital is larger, but that doesn't mean its maternity ward is larger. It also doesn't mean it had a larger sample of births on that day. That's a false assumption. Also there seems to be a hidden assumption that births are equally likely to be boys as girls. This too is not correct, but is at least closer to the truth than the sample size point.

 

So given the information stated, they are equally likely.

[Seeker 11]

Other possible answers to pattuca's riddle (and yes it should have been capitalised, otherwise it's just poorly phrased):

 

Answer: He didn't (seems valid enough to me)

 

Another answer: frist he crossed the bridge one way, then he turned and went over it again, and on the second trip he was technically both crossing and going around the bridge.

 

There is often more than one valid answer. It may not be the answer the riddler had in mind, but it can still be 'correct'.

 

 

Here's a maths puzzle.

 

5 brothers have inheirted 100 million dollars to split up amongst themselves. The brothers are ranked eldest to youngest and it is always the eldest brother who decides how to divide up the inheritance. However, the brothers are democratic: if the oldest brother does not get at least 50% of the vote (including himself), then he is killed and the process repeats itself with the next oldest brother. The brothers are all completely rational (logical) and know that their brothers are too.

 

How does the oldest brother divide up the inheritance to maximise the amount he keeps for himself, i.e. what does he offer to the other brothers?

[addchild 10]

Other possible answers to pattuca's riddle (and yes it should have been capitalised, otherwise it's just poorly phrased):

 

Answer: He didn't (seems valid enough to me)

 

Another answer: frist he crossed the bridge one way, then he turned and went over it again, and on the second trip he was technically both crossing and going around the bridge.

 

There is often more than one valid answer. It may not be the answer the riddler had in mind, but it can still be 'correct'.

 

 

Here's a maths puzzle.

 

5 brothers have inheirted 100 million dollars to split up amongst themselves. The brothers are ranked eldest to youngest and it is always the eldest brother who decides how to divide up the inheritance. However, the brothers are democratic: if the oldest brother does not get at least 50% of the vote (including himself), then he is killed and the process repeats itself with the next oldest brother. The brothers are all completely rational (logical) and know that their brothers are too.

 

How does the oldest brother divide up the inheritance to maximise the amount he keeps for himself, i.e. what does he offer to the other brothers?

 

 

( I have a feeling this is a factorial question but I'm feeling lazy)

 

if they are all rational in the economic sense, then they are self serving. Everyone would vote to kill the oldest for a larger share, until only the two youngest brothers are left and they split it 50m/50m

 

but if they were smart the three eldest brothers would realize this, and sacrifice some of their gains to keep their lives.

 

these arnt exact because im too lazy to do the math during the trading day but

 

1. the oldest would take around 7.5m and divide the rest up roughly

2 would receive around 12.5m

3 would receive around 20m

4 would receive around 30m

5 would receive around 30m (also 5 would receive the same amount as 4, because in the greedy situation where the 3 eldest are killed, the youngest doesn't have greater than 50% of the vote, 4 would except no less than 5).

[Seeker 11]

Good thinking, but not correct. They are all self-serving, and want to maximise the amount they get.

[SIUYA 11]

5 brothers have inheirted 100 million dollars to split up amongst themselves. The brothers are ranked eldest to youngest and it is always the eldest brother who decides how to divide up the inheritance. However, the brothers are democratic: if the oldest brother does not get at least 50% of the vote (including himself), then he is killed and the process repeats itself with the next oldest brother. The brothers are all completely rational (logical) and know that their brothers are too.

 

How does the oldest brother divide up the inheritance to maximise the amount he keeps for himself, i.e. what does he offer to the other brothers?

 

apart from killing each other to keep it all....

 

As the older brother only needs to keep 2 other brothers on side to keep > 50% of the vote.

He can split the inheritance 3 ways to maximise his amount.

3 brothers are happy with $33 mil each , the other 2 have to accept the democratic process.

Basically on this rationale if it was to be split evenly at 20mil each....all you need to do is offer at least two of the brothers a little bit more than that share to get them onside...so it could be as little as 21each to 2 other brothers, screw 2 brothers who have to accept it and keep the remaining 100-(2x21)=$58mil for himself.

 

Too bad ideas of justice and greed get in the way.

[Seeker 11]

apart from killing each other to keep it all....

 

As the older brother only needs to keep 2 other brothers on side to keep > 50% of the vote.

He can split the inheritance 3 ways to maximise his amount.

3 brothers are happy with $33 mil each , the other 2 have to accept the democratic process.

Basically on this rationale if it was to be split evenly at 20mil each....all you need to do is offer at least two of the brothers a little bit more than that share to get them onside...so it could be as little as 21each to 2 other brothers, screw 2 brothers who have to accept it and keep the remaining 100-(2x21)=$58mil for himself.

 

Too bad ideas of justice and greed get in the way.

 

Again, good ideas. Not the right answer though. But on the right track

[BlueHorseshoe 10]

The conclusion that it is the small hospital is incorrect.

 

Hi Seeker,

 

Your points are all quite correct: we can't be certain, and our best guess could involve flawed assumptions.

 

Ignoring the inadequacies of the way I stated the question though, hopefully the point about sample size remains valid.

 

BlueHorseshoe

[Seeker 11]

Hi Seeker,

 

Your points are all quite correct: we can't be certain, and our best guess could involve flawed assumptions.

 

Ignoring the inadequacies of the way I stated the question though, hopefully the point about sample size remains valid.

 

BlueHorseshoe

 

 

Yes, of course, assuming 50% prob male to female births, it's slightly more likely to be the smaller sample size.

 

Let me know if you want the answer to the 5 brother problem.

[TradeRunner 10]

thinking aloud:

 

If it comes down to the 2 youngest brothers then the second youngest walks away with everything...

[Seeker 11]

thinking aloud:

 

If it comes down to the 2 youngest brothers then the second youngest walks away with everything...

 

Yes! And follow that thought through...

[Seeker 11]

So the answer is that:

 

 

 

......

 

 

 

The eldest brother gives brothers 3 and 5, the minimum possible, i.e. if the minimum unit is 1 dollar, he gives them 1 dollar each (if minimum is one cent, he gives them one cent each) and keeps the rest for himself.

 

The reason is: Following from traderunner's thought, you work backwards. If there are two brothers, the elder of the two keeps all the money, because he will get 50% of the vote, and so he walks away with all the money. Extending this to 3 brothers, the youngest of all knows that if he votes against the eldest brothers plan, and the eldest brother loses, then he will walk away with nothing. So he'll accept anything greater than 0 (1 cent, one dollar for example). Brother 3 knows this, so he can offer the one cent to that brother and nothing to the brother in between. This logic works back all the way to the first of 5 brothers.

[SIUYA 11]

i guess pure rationality does not mix with the ideas of justice and fairness.....simply a fear of death v money.

No wonder we have financial crisisisiesiesiiisssss

 

also makes you wonder if the early innovators of inheritance - give it all to the first born male (usually the most aggressive sex) made a lot of sense.

Edited March 19, 2013 by SIUYA

[bobcollett 10]

This is for Patuca....................

[BlueHorseshoe 10]

This is for Patuca....................

 

Third from left?

 

BlueHorseshoe

[Seeker 11]

Third from left?

 

BlueHorseshoe

 

lol, that's what I'd go for too.

[bobcollett 10]

Mr. horseShoes and Seeker, well done , you are smarter thsn me