Puzzles for Traders

[BlueHorseshoe 10]

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

[SIUYA 11]

  BlueHorseshoe said:

 

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

 

top of the head - the smaller one.

why: the larger one is more likely to have a great er number of babies and hence will be more likely to tend toward the average expected of 50%, and hence the smaller one might be more likely to have a number deviate from the expected number.

 

.........................

reminds of this......a logic problem rather than statisitcs - if you want to keep it stats then i apologize.

EASY VERSION of the 'worlds hardest problem'

 

The problem - A fork in a road - one way leads to a village, the other a cliff- is guarded by a liar (false) and a truth teller (true) - you dont know which is which.

 

What single question, demanding a yes or no answer can you ask to find out which road leads to the village and which over the cliff.

 

 

HARD VERSION (The Hardest Logic Puzzle Ever - Wikipedia, the free encyclopedia)

 

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

Boolos (The originator of the question) provides the following clarifications:

• It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
  
• What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
  
• Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
  

[TheDude 10]

The larger one. Because I'm a contrarian.

 

Besides, you didnt say where the hospital was. If it was in the 3rd world (where over half of the worlds population live), there is a high probability ant female births would have been killed at birth and not reported. :helloooo:

[BlueHorseshoe 10]

  TheDude said:

The larger one. Because I'm a contrarian.

 

Besides, you didnt say where the hospital was. If it was in the 3rd world (where over half of the worlds population live), there is a high probability ant female births would have been killed at birth and not reported. :helloooo:

 

"3rd World"? You can't call it that any more! And TPLAC ("Tin Pot Little African Country" - thanks, 'Yes, Minister!') is out as well. Does anyone know what the current politically correct term is? When I was at school it was "Economically Less Developed Country", but that's bound to have changed . . .

 

In Achebe's novels they don't bother killing babies - they place them in a large clay vessel and leave them in the jungle.

 

The closest I have come to the "third world" is Ghana, and there were certainly plenty of women there

 

BlueHorseshoe

[jpennybags 11]

  BlueHorseshoe said:

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

 

I would say the smaller of the two hospitals due to the smaller sample size.

 

By the way... a link to a world map that shows the primary sex ratio (ratio at birth) for each country. Just as a matter of interest, or for those that harbor misconceptions about our 3rd world brothers and sisters:

 

Worldwide Human Sex Ratio at Birth

[bobcollett 10]

Interesting thread , Mr Horseshoes

kind regards

bobc

[BlueHorseshoe 10]

The answer to the last puzzle was, according to current mathematical convention, the smaller hospital due to the smaller sample size.

 

If anyone wants to argue against that, then the ensuing discussion will probably be more interesting than the puzzle itself. The puzzle is taken from Taleb's "The Black Swan", and I personally disagree with the general thesis he promotes, as I think the whole issue he examines is a matter of (retrospectively) ascribing error to a model rather than to the selection of data to which it is applied. On the other hand, Taleb is a big fan of Umberto Eco, one of my favourite authors, so . . .

 

Here's another puzzle:

 

There are 4 shut doors in front of you. You know that each door has an animal painted on one side and a plant painted on the other side. The four doors have the following painted on the sides that you can see (one per door): a lily, a pine tree, a fox, and an eagle. You have been told that these doors satisfy the rule "if a door has a flower on its plant side, then it has a bird on its animal side". What is the smallest set of doors that you must check the hidden side of to determine conclusively whether this rule is true or false for these doors? *

 

1. Just the door with the lily
   
2. Just the door with the eagle
   
3. Just the doors with the lily and the eagle
   
4. Just the doors with the lily and the fox
   
5. Just the doors with the lily, fox and eagle
   
6. Just the doors with the pine tree and eagle
   
7. All of the doors
   

 

This puzzle is taken directly from the application form for a quantitative hedge fund.

 

BlueHorseshoe

[SIUYA 11]

  BlueHorseshoe said:

There are 4 shut doors in front of you. You know that each door has an animal painted on one side and a plant painted on the other side. The four doors have the following painted on the sides that you can see (one per door): a lily, a pine tree, a fox, and an eagle. You have been told that these doors satisfy the rule "if a door has a flower on its plant side, then it has a bird on its animal side". What is the smallest set of doors that you must check the hidden side of to determine conclusively whether this rule is true or false for these doors? *

 

1. Just the door with the lily
   
2. Just the door with the eagle
   
3. Just the doors with the lily and the eagle
   
4. Just the doors with the lily and the fox
   
5. Just the doors with the lily, fox and eagle
   
6. Just the doors with the pine tree and eagle
   
7. All of the doors
   

 

 

I always get these ones wrong - so my Answer in this case is all of the doors.

(I have PMd you my answer so as not to spoil it for anyone.)

............

there is probably an easier way to solve it....

[SIUYA 11]

EASY VERSION of the 'worlds hardest problem'

 

The problem - A fork in a road - one way leads to a village, the other a cliff- is guarded by a liar (false) and a truth teller (true) - you dont know which is which.

 

What single question, demanding a yes or no answer can you ask to find out which road leads to the village and which over the cliff.

 

 

.................

Solution: "If I ask the other person if the left path leads to the village, what would he say?"

 

keep working on the hard one....good luck.

[DeltaTheta 10]

I would think it would be the lily and the eagle. The other two doors violate the premise of flower/bird.

[BlueHorseshoe 10]

  SIUYA said:

Solution: "If I ask the other person if the left path leads to the village, what would he say?"

 

Nice! I didn't get that, despite spending about thirty minutes drawing out a boolean truth table exactly as you did for the doors question.

 

They're always so obvious once you know the answer!

 

Thanks,

 

BlueHorseshoe

[SIUYA 11]

table should be

 

you ask true

if the left path goes to the village --- False would say no so true says NO

if the right path goes to the village ---- False would say yes so true says YES

 

you ask false

if the left path goes to the village --- true would say yes so false says NO

if the right path goes to the village ---- true would say no so false says YES

 

Hence NO = left path, YES=right path regardless of who you ask.

[TradeRunner 10]

  BlueHorseshoe said:

The answer to the last puzzle was, according to current mathematical convention, the smaller hospital due to the smaller sample size.

 

If anyone wants to argue against that, then the ensuing discussion will probably be more interesting than the puzzle itself. The puzzle is taken from Taleb's "The Black Swan", and I personally disagree with the general thesis he promotes, as I think the whole issue he examines is a matter of (retrospectively) ascribing error to a model rather than to the selection of data to which it is applied. On the other hand, Taleb is a big fan of Umberto Eco, one of my favourite authors, so . . .

 

Here's another puzzle:

 

There are 4 shut doors in front of you. You know that each door has an animal painted on one side and a plant painted on the other side. The four doors have the following painted on the sides that you can see (one per door): a lily, a pine tree, a fox, and an eagle. You have been told that these doors satisfy the rule "if a door has a flower on its plant side, then it has a bird on its animal side". What is the smallest set of doors that you must check the hidden side of to determine conclusively whether this rule is true or false for these doors? *

 

1. Just the door with the lily
   
2. Just the door with the eagle
   
3. Just the doors with the lily and the eagle
   
4. Just the doors with the lily and the fox
   
5. Just the doors with the lily, fox and eagle
   
6. Just the doors with the pine tree and eagle
   
7. All of the doors
   

 

This puzzle is taken directly from the application form for a quantitative hedge fund.

 

BlueHorseshoe

 

Lily door: Make sure it has a bird

Eagle door: Doesn't matter what is on the other side as the rule doesn't say anything about the reverse relationship

Fox door: Need to make sure it doesn't have a flower side

Pine tree door: Already on the plant side and not a flower so doesn't matter

 

I think the answer is 4

[Perrin 10]

I'll go for 8 - Lily, Pine Tree, Eagle

 

Is it something like you can never prove something 100%, but you can disprove it. I'm not sure if that's related to this and that's probably not right. Eg this is a letter B <- , yes it is a letter B, proved! But it's something like one instance of an event which disproves the theory is all you need.

 

Anyway:-

You have to open the Lily because it might have a bird type of animal (or another animal which would disprove the theory).

You have to open the Pine Tree for the same reason.

You don't have to open the Fox because it cannot have a ....... no hang on. Pine Tree's wrong.

 

Ok hold on. Let me rethink.

 

Got to check any flowers. We don't have to check any other plant (eg the tree).

 

Lily

Pine Tree

Fox

Eagle

 

So it's answer 5 - you need to open Lily, Fox, Eagle

Lily (if there's not a bird on the back then the theory is wrong)

Pine Tree (can only be an animal on the back so we don't care what type it is)

Fox (it might have a flower on the back)

Eagle (it might not have a flower on the back)

 

 

NO! Hang on, we don't need to open the Eagle do we??? Because if we open the eagle and it has a flower on the back, or if it doesn't, it doesn't aid the proving or the disproving of the theory!!!

 

So it's Lily and Fox, answer number 4!!

 

Edit - I see TradeRunner got here before me - I thought someone would so I didn't look on page 2 before before writing this! Does this mean we get to join a quantitative hedge fund? Please don't tell me they ask more than one question or I'll be here all day

 

(Just imagine how cool it would be if our brains were wired such that we could answer this question immediately, without the need for all the time of working out?!)

[Perrin 10]

Siuya, I've heard the problem that you asked before somewhere, but I still couldn't remember the answer. And even when I read your answer, it still seems so hard to get the solution into my tiny brain.

 

I'm not sure I like this thread. I didn't get into trading to solve complicated puzzles and problems!

 

[bobcollett 10]

The answer is 1

bobc

[Patuca 13]

a man came to a bridge that crossed a railroad track. he went across the bridge but yet went around the bridge at exactly the same time. how did he do it?

Edited January 11, 2013 by Patuca

[SIUYA 11]

stumbled on this....not so much a brain teaser- or is it?

http://www.traderslaboratory.com/forums/general-discussion/4420-test-your-tool.html

 

Also Traderunner you might be best to answer this....or anyone else.

your answers thoughts....

 

Lily door: Make sure it has a bird

Eagle door: Doesn't matter what is on the other side as the rule doesn't say anything about the reverse relationship

Fox door: Need to make sure it doesn't have a flower side

Pine tree door: Already on the plant side and not a flower so doesn't matter

I read the quote ""if a door has a flower on its plant side, then it has a bird on its animal side" as a rule, and hence the inverse relationship must also be true......

my question was more along the lines of is this what is referred to as 'known known or unknown knowns' - or something similar i have heard this before apart from Donald Rumsfeld.

Refering to the point that you can see one side of the doors, and its irrelevant to think about if you were on the other side of the doors.

thanks

(the things that pop into my head while at the gym)

[SIUYA 11]

  Patuca said:

a man came to a bridge that crossed a railroad track. he went across the bridge but yet went around the bridge at exactly the same time. how did he do it?

 

it was a different day - same time.

[jpennybags 11]

  BlueHorseshoe said:

Here's another puzzle:

 

There are 4 shut doors in front of you. You know that each door has an animal painted on one side and a plant painted on the other side. The four doors have the following painted on the sides that you can see (one per door): a lily, a pine tree, a fox, and an eagle. You have been told that these doors satisfy the rule "if a door has a flower on its plant side, then it has a bird on its animal side". What is the smallest set of doors that you must check the hidden side of to determine conclusively whether this rule is true or false for these doors? *

 

1. Just the door with the lily
   
2. Just the door with the eagle
   
3. Just the doors with the lily and the eagle
   
4. Just the doors with the lily and the fox
   
5. Just the doors with the lily, fox and eagle
   
6. Just the doors with the pine tree and eagle
   
7. All of the doors
   

 

This puzzle is taken directly from the application form for a quantitative hedge fund.

 

BlueHorseshoe

 

I first answered this with the assumption that the hidden side of the doors used the same symbols as the known side... each symbol used once. In that case the answer would be #3. That is not how the text reads though... there is no mention of what is on the hidden side or what symbols are used. The symbols may be entirely different symbols, or the symbols can be used more than once. If that is the case then all the doors must be opened.

[TradeRunner 10]

I'm not sure I understand your question but I disagree with

 

  SIUYA said:

""if a door has a flower on its plant side, then it has a bird on its animal side" as a rule, and hence the inverse relationship must also be true......

 

 

The rule doesn't say

 

if a door has a bird on its plant side, then it has a flower on its plant side

 

For example if I had a door with an eagle on its animal side and an Oak on its plant side then the original rule would not be broken

 

Programming wise the first rule could be enforced with

IF plant side is a flower THEN

Assert animal side is a bird

 

but to enforce the bidirectional rule then you would need

 

IF plant side is a flower THEN

Assert animal side is a bird

IF animal side is a bird THEN

Assert plant side is a flower

 

More code and more words in the rule would be required (IMO).

 

Makes you wonder what the interviewer is trying to assess by asking this type of questions. The question is asked on an application form so the candidate doesn't have to think on their feet.

 

TradeRunner

[SIUYA 11]

thanks - helps to think more in terms of programming rather than scenarios.....

The if ...then not if... or ...then

A reason why i was never good at these

[addchild 10]

  BlueHorseshoe said:

The answer to the last puzzle was, according to current mathematical convention, the smaller hospital due to the smaller sample size.

 

If anyone wants to argue against that, then the ensuing discussion will probably be more interesting than the puzzle itself. The puzzle is taken from Taleb's "The Black Swan", and I personally disagree with the general thesis he promotes, as I think the whole issue he examines is a matter of (retrospectively) ascribing error to a model rather than to the selection of data to which it is applied. On the other hand, Taleb is a big fan of Umberto Eco, one of my favourite authors, so . . .

 

Here's another puzzle:

 

There are 4 shut doors in front of you. You know that each door has an animal painted on one side and a plant painted on the other side. The four doors have the following painted on the sides that you can see (one per door): a lily, a pine tree, a fox, and an eagle. You have been told that these doors satisfy the rule "if a door has a flower on its plant side, then it has a bird on its animal side". What is the smallest set of doors that you must check the hidden side of to determine conclusively whether this rule is true or false for these doors? *

 

1. Just the door with the lily
   
2. Just the door with the eagle
   
3. Just the doors with the lily and the eagle
   
4. Just the doors with the lily and the fox
   
5. Just the doors with the lily, fox and eagle
   
6. Just the doors with the pine tree and eagle
   
7. All of the doors
   

 

This puzzle is taken directly from the application form for a quantitative hedge fund.

 

BlueHorseshoe

 

Only open the doors with the lily and the fox.

 

You need to prove that a bird IS on the other side of the lily, and that a flower ISN'T on the other side of the fox.

[TradeRunner 10]

Here is a "simple" probability problem:

 

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

[BlueHorseshoe 10]

TradeRunner has it!

 

It's interesting how many different ways people think about these things. I don't mean in terms of the answer they reach, but in terms of the process they use.

 

Most of the confusion is about the difference between material implication and material equivalence - presumably this is what the question was intended to test. Using the initials of each item it should look like this:

 

P = F ⇒ A = B

 

This is not logically equivalent to:

 

A = B ⇒ P = F

 

If the two are equivalent rather than just one implying the other, then a two-way arrow is used in notation.

 

So here's another puzzle as an extension of this:

 

Why, if for a function f, if it it true that:

 

x = 4 ⇒ f(x) = 16

 

Is it false that:

 

f(x) = 16 ⇒ x = 4

 

???

 

BlueHorseshoe