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   Author  Topic: new york times problem solving test  (Read 1109 times)
towr
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new york times problem solving test  
« on: Aug 25th, 2015, 8:39am »
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Might be a bit too easy, but it's cute.
 
http://www.nytimes.com/interactive/2015/07/03/upshot/a-quick-puzzle-to-t est-your-problem-solving.html
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Re: new york times problem solving test  
« Reply #1 on: Aug 25th, 2015, 9:45am »
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The perils of finding a formula for a finite series ...
 
Being a C programmer guess what "the rule" I came up with when is saw 21, 22, 23.
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Re: new york times problem solving test  
« Reply #2 on: Aug 25th, 2015, 11:25am »
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The real trick is not so much figuring out a suitable rule, as figuring out ways to test potential rules...
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Re: new york times problem solving test  
« Reply #3 on: Sep 1st, 2015, 6:56pm »
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So, how many of us intentionally tried getting a "No" ? How many "No"s did you try to get before you were  satisfied with the 'rule' ?
 
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Re: new york times problem solving test  
« Reply #4 on: Sep 1st, 2015, 10:15pm »
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I can't remember how many "no"s I tried for. But after the initial "successive powers of two" phase I did test for "geometric sequence", "anything goes", "strictly monotonically increasing", "weakly monotonically increasing", "strictly monotonic", "weakly monotonic".
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Re: new york times problem solving test  
« Reply #5 on: Sep 2nd, 2015, 9:02am »
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on Sep 1st, 2015, 6:56pm, JiNbOtAk wrote:
So, how many of us intentionally tried getting a "No" ? How many "No"s did you try to get before you were  satisfied with the 'rule' ?
 

 
It's been a while since I first came across it, but I got something like 4 "no"s before settling on "strictly increasing numbers" with a general approach of trying to find boundaries between "yes" and "no" rather than trying to get easy "yes"es
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Re: new york times problem solving test  
« Reply #6 on: Sep 2nd, 2015, 10:20am »
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I've got at least 4 "no"s: tried reversing the sequence as 8, 4, 2. Then 3, 9, 27. Then 27, 9, 3. Then rearranging the numbers: 4, 8, 2 and 9, 27, 3 etc.
 
I think that on this forum you are dealing with, in general, a rather specific bunch: as a C(Java) Solaris/CentOS programmer I can say that codewise - especially the more you move away from the raw academic compsci code - before you get to a "yes" and return you step through a fair amount of "no"s and after a while it's in our blood.
 
My family sometimes calls me "doom and gloom". Well. It's not doom and gloom. If it can go wrong - it will. So it's error/edge/boundary conditions/special cases handling ...
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Re: new york times problem solving test  
« Reply #7 on: Sep 3rd, 2015, 7:19pm »
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I did not start with what I should have, i.e. a global approach of searching yesses and nos.
 
Instead, I saw the pattern 2k and tried to generalize it.  I tried  a*2k  and  a*bk.  Only then I tried sequences that don't translate to a closed formula.
 
I quickly accepted "strictly increasing" because I realized the point of the exercise was best made with the simplest rule and monotonic was the simplest I could think of.  I checked whether it is strictly increasing or not.
 
One explanation of what happens would be that we are usually asked to recognize a sequence.  Once the idea of "powers of two" came to us, we have to first kill that idea before searching more globally.
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