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One thing I learned when doing Brilliant problems

If it says "put \(x\) as the answer if ..." in the clarification, then \(x\) is not the answer.

Note by Daniel Wang
3 years, 9 months ago

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Your statement is not necessarily true. Calvin Lin Staff · 3 years, 9 months ago

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@Calvin Lin Next week, be sure to try \(x\) for all problems with such a clarification :) Daniel Chiu · 3 years, 9 months ago

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@Daniel Chiu thats a good idea Tyler Gold · 3 years, 9 months ago

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I actually learn something a little bit different. For example,

  • "The answer can be expressed as \(\dfrac{a}{b}\), where \(a,b\) are coprime positive integers. Find \(a+b\)." usually means \(b \neq 1\), otherwise they will ask for the answer straight away.
  • "Find the last three digits of the answer." usually means the answer is greater than or equal to \(1000\), otherwise they will ask for the answer straight away.

Note all "usually"s appearing there, so don't blame me for blindly following the above. Ivan Koswara · 3 years, 9 months ago

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@Ivan Koswara Likewise, not necessarily true. I do try and avoid allowing you to make such generalizations. The assumption that the answer must be an integer from 0 to 999 is introduced for simplicity in explanation. We might remove that condition in future, and use the Physics style of "real numbers" instead.

If a value is 'clearly' in the form of a fraction (e.g. expected value, lots of division going on, etc) I often ask in terms of a fraction, even if the answer turns out to be an integer. Though, to be fair, this is much rarer.

If a value is 'potentially' huge (e.g. find the sum of all numbers which satisfy this condition), I often ask for the last three digits. I've received numerous disputes saying that "but the answer must be more than 1000, so you are wrong". Calvin Lin Staff · 3 years, 9 months ago

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@Calvin Lin Well, I rarely see problems that disprove the above claims, and I do claim "usually", so my claims still stand. But I've never deduced in that way anyway.

A related note, a problem just last week: "Find the sum of all \(a\) satisfying the condition." I got one possible value of \(a\) that was a fraction; everything else were integers. I had the strong urge to dismiss that fractional value by "if that fractional value is a possible value of \(a\), then the answer of this question will not be an integer". Ivan Koswara · 3 years, 9 months ago

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@Ivan Koswara Actually for the second one, it quite often is less than \(1000\), but simply is there to not have you discount the possibility that it is greater than \(1000\) (which can, conceptually, be a huge indicator in problems of the scope you're dealing with) Michael Tong · 3 years, 9 months ago

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@Ivan Koswara I know you said 'usually' but here is a counterexample to the second point.

<https://brilliant.org/assessment/s/number-theory/5045346/> Cole Coupland · 3 years, 9 months ago

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Okay, I notice the "IF", but why "x" is not the answer? Selene (Elly) Kirkland · 3 years, 9 months ago

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@Selene (Elly) Kirkland well.. it could've said put x if x is greater than or equal to 0 else put x + 1000. Taehyung Kim · 3 years, 9 months ago

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guys, pls anyone tell me! how do I create a challenge? thanks, john John Bakradze · 3 years, 9 months ago

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@John Bakradze You can't now that they removed the option to submit problems. Ryan Soedjak · 3 years, 9 months ago

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@Ryan Soedjak I know i really liked that :( Tyler Gold · 3 years, 9 months ago

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They want x as the answer in the first place, so why is it NOT the answer? I don't get you. EDIT: Assuming the 'if...' is proven true in the question. Yuxuan Seah · 3 years, 9 months ago

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@Yuxuan Seah

Assuming the 'if...' is proven true in the question.

It usually isn't true. Ryan Soedjak · 3 years, 9 months ago

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