Problem 118

estanford · Post by **estanford** » Fri Feb 19, 2010 10:41 am

Problem 118 asks about distinct sets containing each of the digits one through nine exactly once. Are we free to assume that the sets contain only those digits, or might they include the digit zero?

ThomasH · Post by **ThomasH** » Fri Feb 19, 2010 10:49 am

estanford wrote: ... or might they include the digit zero?

Definitively not.

estanford · Post by **estanford** » Fri Feb 19, 2010 11:12 am

Got it. I just reread the problem statement and noticed that the possibility was excluded by the set construction rule.

Francky · Post by **Francky** » Sat Jun 25, 2011 8:23 pm

I'm proud of my algo
2.9s of uncompiled Python. (No extern help like prime file...)

spacetweek · Post by **spacetweek** » Wed Oct 19, 2011 1:42 pm

Is there a minimum number of elements that the set has to contain?

Francky · Post by **Francky** » Wed Oct 19, 2011 1:50 pm

spacetweek wrote:Is there a minimum number of elements that the set has to contain?

A set with one single element could be valid.

eagle33199 · Post by **eagle33199** » Fri Aug 24, 2012 4:56 am

*edit*

Never mind, I just found my issue. I reduced my search space to only include the numbers 1-4 (only 9 results), which made it small enough to figure out by hand which items I was missing, and then track down why.

thedoctar · Post by **thedoctar** » Sun Sep 23, 2012 5:02 pm

OH MY GOD!!!! It has taken me an hour to realise that {1, 2} is not distinct from {2, 1}. I'm so used to the problem giving examples and defining distinctness. Might I ask for examples of distinct sets and indistinct sets to be given so that others won't fall into the same mistake as mine?

euler · Post by **euler** » Sun Sep 23, 2012 5:39 pm

A set is described by the unique unordered elements it contains. So, for example, the sets {1,4,9}, {1,4,1,9,1}, and {9,1,4} are identical as the order of the elements is irrelevant and each set essentially contains the elements 1, 4, and 9. Certainly for comparison it is helpful to list elements in some logical order, but it is not necessary. Remember elements of a set do not need to be numbers and can be data/objects of any type, which can make ordering in some cases subjective.

I don't think it is practical to define every standard mathematical term we use. However, I would say that we do need to define terms when there is any possibility of ambiguity, or when we wish to take liberties with the accepted understanding of the mathematical terms.

If you can find a recognised source which says that in some cases {1,2} and {2,1} are considered distinct or if others feel that there is sufficient cause for confusion in this particular problem then I will gladly modify the problem wording. But we must be careful not to open the floodgates of adding pages of footnotes to every problem.

thedoctar · Post by **thedoctar** » Mon Sep 24, 2012 12:11 pm

euler wrote: If you can find a recognised source which says that in some cases {1,2} and {2,1} are considered distinct or if others feel that there is sufficient cause for confusion in this particular problem then I will gladly modify the problem wording. But we must be careful not to open the floodgates of adding pages of footnotes to every problem.

Yes I understand this, I rushed through reading the problem and as I said, previous problems have given examples of distinctness and I was so accustomed to this that I totally ignored the fact that sets had to be distinct and it took me so long to find this mistake.

I don't want to be any trouble, but maybe problems where little details like only counting distinct sets could be bolded, which won't add any text to the problem but will prevent people reading over those details?

thundre · Post by **thundre** » Mon Sep 24, 2012 2:43 pm

I don't think there is any ambiguity here. "Set" is a well-defined mathematical term. The word "distinct" appears in the problem statement even though it is unneccessary. For someone to think they had to count all permutations of each set seems like a rare misinterpretation.

thedoctar · Post by **thedoctar** » Wed Sep 26, 2012 8:48 am

Okay, well if it's just me and my strange interpretation you don't have to change anything, I just didn't read question properly I guess.

pimspelier · Post by **pimspelier** » Thu Oct 23, 2014 5:19 pm

I've got a question. After looking at my Python code for some time, I have removed some bugs, but still get the red cross

. Can I PM someone with my code, since I have no idea what I might be doing wrong. I count each set only once, so that's not the problem.

Arthelais · Post by **Arthelais** » Thu Oct 23, 2014 10:19 pm

pimspelier wrote:I've got a question. After looking at my Python code for some time, I have removed some bugs, but still get the red cross . Can I PM someone with my code, since I have no idea what I might be doing wrong. I count each set only once, so that's not the problem.

Send it through!

solarmew · Post by **solarmew** » Mon Jan 26, 2015 1:36 pm

could i also please have someone look at my code? >.> ... i've double checked it several times, i feel like it should work %\

Bubbler · Post by **Bubbler** » Mon Jan 26, 2015 1:51 pm

What language are you using?

solarmew · Post by **solarmew** » Mon Jan 26, 2015 2:19 pm

nm, found the problem +.+

Chimerade · Post by **Chimerade** » Tue Sep 12, 2017 8:30 am

Hi,

Is 1 considered as prime in problem 118 ?

Thank You

LilStalker · Post by **LilStalker** » Tue Sep 12, 2017 8:44 am

1 will never be considered a prime number since it is not a prime number.

Chimerade · Post by **Chimerade** » Tue Sep 12, 2017 10:06 am

Thank You !

I was not up to date on this question... You are right ! Thank you for a very quick answer

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