Jump to content

Welcome to the new Traders Laboratory! Please bear with us as we finish the migration over the next few days. If you find any issues, want to leave feedback, get in touch with us, or offer suggestions please post to the Support forum here.

  • Welcome Guests

    Welcome. You are currently viewing the forum as a guest which does not give you access to all the great features at Traders Laboratory such as interacting with members, access to all forums, downloading attachments, and eligibility to win free giveaways. Registration is fast, simple and absolutely free. Create a FREE Traders Laboratory account here.

BlueHorseshoe

Puzzles for Traders

Recommended Posts

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.

Share this post


Link to post
Share on other sites

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?

Share this post


Link to post
Share on other sites
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).

Share this post


Link to post
Share on other sites

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.

Share this post


Link to post
Share on other sites
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

Share this post


Link to post
Share on other sites
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

Share this post


Link to post
Share on other sites
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.

Share this post


Link to post
Share on other sites

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.

Share this post


Link to post
Share on other sites

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

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 by SIUYA

Share this post


Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.


  • Topics

  • Posts

    • @sxiqxx, Well done on making your first post a promising strategy. @everyone, post up if you want this coded into an EA. Although I switched to TradeStation, I still have an active MT5 demo with MetaEditor. I can code it without referencing object oriented programming which should be retroactively compatible with MT4. Let me know...
    • Please allow me to retort (in jest): RESPONSE 1 : Get a job supervising others where you're in control of performance reports and ride those others 100%. This makes your performance 100% with little to no effort.   RESPONSE 2: Feel free to piss off your boss but stay nonviolent. When the side effects of his viagra and testosterone boosters cause him to physically assault you, you have the legal upper hand. This can result in a boatload of trading capital.   RESPONSE 3: Feel free to have intimate relations with your boss if she finds you attractive. Rest assured that mum's the word because once again, you have the legal upper hand. This can also result in a boatload of trading capital.   RESPONSE 4: Don't be fake friends with any enemies... unless you need information from them. Being fake friends with everyone will cause you to become an empty shell of a person with no direction in life.   REPONSE 5: Get your boss to become reliant on your performance (really, just the performance of your subordinates), and then plan an "overheard" conversation wherein you fake an interview with another potential employer. You'll probably get a pay increase or a promotion.   RESPONSE 6: If you can give your 75% percent to a project, give 50% and rely on your legal upper hand(s). Learn to write trading algo's during your other 50%.   RESPONSE 7: Take all of the office boys out to nightclub where you merely sip soft drinks on a weeknight. Upon your return to the office in the morning, inform the security guards that all of the office boys are intoxicated. Your boss will love you for it.   RESPONSE 8: Never try to prove your client wrong or find faults in their processes, but do secretly collect their information in case you jump ship or "someone you know" decides to start his own company.   RESPONSE 9: Never stay in a firm for too long. Instead, use your ill-gotten capital to exit the rat-race and start trading.   RESPONSE 10: Trading pays more than your career. Interpersonal skills are now irrelevant. Use your technical skills for trading. Never stop learning and keep updating your technical skills.😁
    • There are a lot of trading strategies like elliot waves, wyckoff etc so we need to apply those who best suited to our need and are understandable too.
    • Scalping can be good during the high volatile markets however the new traders should be careful while entering and exiting the markets too quickly since they can make losses as well. If the broker support news trading we can make most out of the scalping in my opinion.  
    • In my opinion these candlestick charts are more easier to understand as compared with the other charts.
×
×
  • Create New...

Important Information

By using this site, you agree to our Terms of Use.