Test Your Problem Solving Skills with Fun Quiz

[Ygggdrasil]

Here's a fun little quiz to test your problem solving skills. It's something I'd recommend all scientists or aspiring scientists take a shot at, as I learned a lot by taking the quiz: http://www.nytimes.com/interactive/...uick-puzzle-to-test-your-problem-solving.html

It's probably best to try the quiz first before reading comments that will probably have spoilers.

 

[Tobias Funke]

Man, I come up with an incorrect rule that works for the given sequence, confirm it twice and then submit it because getting it wrong means literally nothing to me, and all of a sudden I'm just like Cheney invading Iraq? That's harsh, Times.

 

[Intrastellar]

Veritasium made a very nice video about this quiz. Watch it only after trying the quiz yourself.

 

[Enigman]

I got it, but I faintly remember seeing this one before.

Edit: This explains it:

This experiment is a version of one that the English psychologist Peter Cathcart Wason used in a seminal 1960 paper on confirmation bias.

 

[Borek]

Felt into a trap of confirming first rule that got "yes", instead of trying to check if other rules don't work. But I am not convinced it was a hunt for more "yeses".

 

[256bits]

Were we to answer by giving all the rules that the sequence follows - there are at least 2 more, giving 3 sequence rules.
And a fourth that is not a sequence in the normal sense but considers ordering.

I was just trying to guess what rule he had in mind.
The writer lists only one rule.
Is that fair?

 

[Enigman]

You were allowed as many trial sequences as you wanted, so for the purposes of the test, yes?

This investigation examines the extent to which intelligent young adults seek (i) confirming evidence alone (enumerative induction) or (ii) confirming and discontinuing evidence (eliminative induction), in order to draw conclusions in a simple conceptual task. The experiment is designed so that use of confirming evidence alone will almost certainly lead to erroneous conclusions because (i) the correct concept is entailed by many more obvious ones, and (ii) the universe of possible instances (numbers) is infinite.

http://www.tandfonline.com/doi/abs/10.1080/17470216008416717#.VZes51JG-So

 

[zoobyshoe]

Well, since the original sequence was all even numbers, I thought it prudent to check if the rule allowed odd numbers and tried a sequence that began with 13. I was prepared to get a "no" on that, but got a "yes" so I thought the rule was probably exactly what it seemed to be. It didn't occur to me to check any other rule because the three numbers were described as a "sequence." That meant it had to be either an arithmetical or geometric sequence. Given 2,4,8, which kind of a sequence was I supposed to think it was, eh?

The numbers 2, 37, 999, would follow their "rule," but can they actually be described as a "sequence"?

 

[Ygggdrasil]

The relevant lesson from this experiment for scientists is the importance of negative controls. 78% of people submit an answer without receiving a negative answer (I was among that 78% as well). However, those who think to test a negative case will quickly catch on to the trick. I'm less convinced about the connection to a desire to hear only yes answers, but the results certainly show that most people don't consider the possibility that their initial guess is wrong.

 

[Borek]

The numbers 2, 37, 999, would follow their "rule," but can they actually be described as a "sequence"?

I don't see why not. Sequence is just a list of numbers, there are no conditions saying it has to be arithmetical or geometrical.

 

[zoobyshoe]

I don't see why not. Sequence is just a list of numbers, there are no conditions saying it has to be arithmetical or geometrical.

You're saying in math, any random list of numbers can be described as a "sequence"? If so, I have never encountered this. Math books I've seen speak only of arithmetical or geometric sequences.

 

[256bits]

The relevant lesson from this experiment for scientists is the importance of negative controls. 78% of people submit an answer without receiving a negative answer (I was among that 78% as well). However, those who think to test a negative case will quickly catch on to the trick. I'm less convinced about the connection to a desire to hear only yes answers, but the results certainly show that most people don't consider the possibility that their initial guess is wrong.

I'll agree that most people will look for a mathematical formula just do to pre-conceived ideas ingrained in their brains.
What about a youngster? At a certain age I would say they would say the next number is a "9" in the sequence.
Interesting about the "yes" reinforcement.
Better on some days than others, I would suppose also.

 

[Dembadon]

You're saying in math, any random list of numbers can be described as a "sequence"? If so, I have never encountered this. Math books I've seen speak only of arithmetical or geometric sequences.

To my knowledge, in mathematics, a sequence can be (informally) defined as an ordered set. The set does not have to contain numbers; its elements can be whatever you want (letters, mammals, colors, etc.).

Edit: removed incorrect information

 

[JonnyG]

You're saying in math, any random list of numbers can be described as a "sequence"? If so, I have never encountered this. Math books I've seen speak only of arithmetical or geometric sequences.

Yes. A sequence of real numbers is a list of real numbers. It need not have any pattern. That's why I hate questions which ask me to guess what the next number in a given sequence is. How would I know?! It could be anything. It's your sequence, you have to tell me!

 

[WWGD]

Yes, a sequence is a collection indexed by any subset of {1,2,3,...}. The problem is that there is too little data to draw a strong conclusion.
Over -reaching, I would say.

 

[Dembadon]

Yes. A sequence of real numbers is a list of real numbers. It need not have any pattern. That's why I hate questions which ask me to guess what the next number in a given sequence is. How would I know?! It could be anything. It's your sequence, you have to tell me!

While a sequence does not always have to follow a pattern (other than it being ordered), the fact that you're asked what the next element in the sequence is implies that it cannot be anything, and that some rule/pattern exists for the set.

 

[WWGD]

While a sequence does not always have to follow a pattern (other than it being ordered), the fact that you're asked what the next element in the sequence is implies that it cannot be anything, and that some rule/pattern exists for the set.

The/a problem is that, with the information given, there are _infinitely many_ possible patterns. You assume the writer is another person who believes the data given uniquely describes the sequence , and you go along with it because that is what you get most of the time, people who have this (wrong) belief.

 

[PeroK]

You're saying in math, any random list of numbers can be described as a "sequence"? If so, I have never encountered this. Math books I've seen speak only of arithmetical or geometric sequences.

Those are the most common sequences that you might meet in high-school maths, but as @Borek says, a sequence can have any numbers in any order. In fact, more generally, you could have a sequence of other mathematical objects, such as a sequence of functions or a sequence of sets.

You could check out the Bolzano-Weierstrass Theorem for a fascinating result on (bounded) sequences in general:

https://en.wikipedia.org/wiki/Bolzano–Weierstrass_theorem

 

[WWGD]

To belabor the point a bit more, an example of objects that cannot be arranged or described as a sequence, is that of all the Real numbers is an interval like [0,1]; you cannot list them as having a 1st, 2nd, ...nth term, and describe them exhaustively.

 

[Dembadon]

The/a problem is that, with the information given, there are _infinitely many_ possible patterns. You assume the writer is another person who believes the data given uniquely describes the sequence , and you go along with it because that is what you get most of the time, people who have this (wrong) belief.

It depends on whether the set is finite, and how many elements one is asked to find. For the exercise in question, I believe your are correct that there is not enough information given to treat the exercise rigorously.

 

[WWGD]

It depends on whether the set is finite, and how many elements one is asked to find. For the exercise in question, I believe your are correct that there is not enough information given to treat the exercise rigorously.

And this is the problem I have with many quizzes, and even some TV shows, like "What Would you Do", with Quinones: there is no real control in the
experiment; it is poorly --if at all --thought out. But the worse part is that it wants to come off as scientific/meaningful without putting the effort to get there. They should just admit from the get go that the test is not scientific.

 

[Dembadon]

... a sequence can have any numbers in any order.

That sequences do not have to be ordered is new to me. I admit to a great deal of mathematical ignorance, though.

 

[PeroK]

That sequences do not have to be ordered is new to me. I admit to a great deal of mathematical ignorance, though.

A sequence itself is an ordered set but the terms need not be in any particular order.

If you take a finite sequence of say the squares:

1, 4, 9, 16

Then that incidentally is neither an arithmetic nor geometric sequence. But those numbers in any other order are still a sequence.

9, 1, 4, 16

Is another valid finite sequence.

 

[Dembadon]

A sequence itself is an ordered set but the terms need not be in any particular order.

If you take a finite sequence of say the squares:

1, 4, 9, 16

Then that incidentally is neither an arithmetic nor geometric sequence. But those numbers in any other order are still a sequence.

9, 1, 4, 16

Is another valid finite sequence.

That has been my understanding. Thank you for the explanation; I misunderstood the way in which you used 'order'.