Project Euler Forum

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?

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

Definitively not.

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

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

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

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

A set with one single element could be valid.

*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.

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?

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.

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?

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.

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.

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.

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!

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

What language are you using?

nm, found the problem +.+

Hi,

Is 1 considered as prime in problem 118 ?

Thank You

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

Thank You !

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