# Thread: Simple puzzles to stump people

1. Originally Posted by Jennifer
Well, part of the stipulation is that everyone shakes a different number of hands.
That makes it far too complex for me calculate, I don't understand how to include that part of it to see a clearer answer. I'll let you handle this one.

2. Originally Posted by athenian200
There are 4 people total.

Nonpareil may shake hands with everyone except herself and ptgatsby.

Nonpareil may shake hands with 2 people.

Each of the others may shake hands with only 1 person (Nonpareil) if ptgatsby is not included as a potential shaker, and 2 people if he is.

I don't see where I'm going wrong.
4 people. Yes.

pt could shake hands, he just didn't ask himself the howmany hands he shook, so the number of hands he shook is a parameter we can play with the make the other numbers work.

So there are 4 people:

Nonpareil
ptgatsby
guest1
guest2

The maximum number of hands any of them could shake is 2, the minimum is 0.

Out of these three people:
Nonpareil
guest1
guest2

you need say which one shook hands with 0, which one with 1, and which one with 2. Note, as far as constraints either guest1 or guest2 could have shaken hands with pt, but Nonpareil couldn't have. Also, guest1 did not shake hands with guest2.

I hope it is clearer now.

3. Originally Posted by athenian200
... I'll let you handle this one.
<-- my brain

Oh, wait... doh!

All right.

In this situation (spoiler):

- If Guest 2 shakes no hands, Non cannot shake her hand either (for a total of 0).
- Non shakes Guest 1's hand and no others. (for a total of 1)
- Guest 1 shakes PT's and Non's hands (for a total of 2)

So for one other couple:
PT: 1
Non: 1
Guest 1: 2
Guest 2: 0

4. Originally Posted by ygolo
Familiarity, and familiarity of use are two different things. No offense but learning something in a school context is very different from having a technique in your repertoire that you apply to work, and perhaps seeps in to everyday thinking.
No offense taken. You just might be right that familiarity in concrete application breeds better performance. Though I personally suspect it is mostly a case of there being two kinds of people in the world, those who are naturally vaccinated against the (so-called) base rate fallacy, like you (?), pt (Edit: and Santtu ) and the INTP in my class who said he knew to use Bayes' Rule but didn't bother doing the math in his head, and the rest of us. (And of course the first group would be more prone to end up in work requiring said application.)

The 12&#37; answer is an example of using an intermediate number as the answer it self. Were 17% and 29% also common incorrect answers?
Unfortunately I don't remember, but I don't think so.

I found that funny also. But I think that has to do with the style of probability education received by those PHDs. Some times people just learn mechanisms without understanding the notions behind them. If people were taught the Long-Run Frequency interpretation of probability, then they would automatically prune the tree to situations they needed, instead of attempting a complcated and error prone application of Bayes' Rule.

But still, I am always amazed when people I think would generally get these types of problems, miss them. So, I probably just shot down my own theory.
A great element of the class I attended consisted in the stories the professor (who is a cutting edge researcher in this field) could and did tell of top economists who themselves have committed the various fallacies that they refused to believe that people (like, vox populi - never mind the mathematically literate elite) are capable of committing systematically. His bemusement ended up being infectious (once we had recovered from swallowing the egos he had proven to be irrational, that is ).

5. Originally Posted by Jennifer
<-- my brain

Oh, wait... doh!

All right.

In this situation (spoiler):

- If Guest 2 shakes no hands, Non cannot shake her hand either (for a total of 0).
- Non shakes Guest 1's hand and no others. (for a total of 1)
- Guest 1 shakes PT's and Non's hands (for a total of 2)

So for one other couple:
PT: 1
Non: 1
Guest 1: 2
Guest 2: 0

Yup. You could, of course, swap guest 1 and guest 2.

Now, can you solve the original puzzle?

6. Originally Posted by ygolo
Now, can you solve the original puzzle?
For two other couples (6 people altogether), I got this (spoiler below):

PT: 1
Non: 3
Guest 1: 1
Guest 2: 2
Guest 3: 4
Guest 4: 0

If I project that pattern out to 22 people, that would leave Non shaking the hands of 19 people.

7. Originally Posted by athenian200
On the card problem, my guess was that if I could only turn over one card, I would choose "A." Was that a good guess or bad one? But I believe that I would actually have to turn over every card besides "B" in order to be completely certain.

I still don't understand the Hall problem. It seems to be based on probability. My understanding is that if you choose any particular door, and then one of the other non-car doors is eliminated, then you have two choices, one of which is the car, and one of which is the goat. No matter which door you choose, the one that you previously chose, or the other, you still have a 1 in 2 chance of winning the car. I don't understand the answers they came up with.
Same here. In the Wason card problem, I don't see any reasoning for a card other than A, and the Monty Hall problem seems to be a simple 50/50 chance. The only complication I can see is a tell from the host, which isn't addressed. Is it possible that this is a case of lies, damned lies, and statistics?

8. Originally Posted by FMWarner
Same here. In the Wason card problem, I don't see any reasoning for a card other than A, and the Monty Hall problem seems to be a simple 50/50 chance. The only complication I can see is a tell from the host, which isn't addressed. Is it possible that this is a case of lies, damned lies, and statistics?
You have to turn over the 7 to see if there's a vowel on the other side. If there is, it disproves the hypothesis.

And your assignment is to disprove the hypothesis.

9. Originally Posted by Jennifer
For two other couples (6 people altogether), I got this (spoiler below):

PT: 1
Non: 3
Guest 1: 1
Guest 2: 2
Guest 3: 4
Guest 4: 0

If I project that pattern out to 22 people, that would leave Non shaking the hands of 19 people.
I don't think that's quite correct.

Guest 3 shook hands with pt, Non, Guest 1 and Guest 2.
Guest 4 with nobody.
Guest 2 shook hands with Guest 3, and Non
Guest 1 shook hands with guest 4? or Non?

10. Originally Posted by Economica
No offense taken. You just might be right that familiarity in concrete application breeds better performance. Though I personally suspect it is mostly a case of there being two kinds of people in the world, those who are naturally vaccinated against the (so-called) base rate fallacy, like you (?), pt (Edit: and Santtu ) and the INTP in my class who said he knew to use Bayes' Rule but didn't bother doing the math in his head, and the rest of us. (And of course the first group would be more prone to end up in work requiring said application.)
It just hit me where this might of come from - I did a lot of research into how the base rate fallacy applied to brokers, funds and so forth back when I was into finances.

Likewise, I probably don't have the same degree of critical thinking/familiarity with practical problems to solve the card problem since it's never been something I've used in my life. In thinking about it, I don't think I can come up with a practical analogy to the card problem... The hall problem I've worked with directly before so I can't really say much for sure there.

I suspect this is significantly different than technical and educational goers... I deviate from the norm along the lines of how I learnt it and how I applied it, the two factors that would seem to matter!

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