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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.

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".

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".

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)

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

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## Comments

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TopNewestYour statement is not necessarily true.

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Next week, be sure to try $x$ for all problems with such a clarification :)

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thats a good idea

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

Note all "usually"s appearing there, so don't blame me for blindly following the above.

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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".

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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".

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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)

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

<https://brilliant.org/assessment/s/number-theory/5045346/>

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Okay, I notice the "IF", but why "x" is not the answer?

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well.. it could've said put x if x is greater than or equal to 0 else put x + 1000.

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guys, pls anyone tell me! how do I create a challenge? thanks, john

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You can't now that they removed the option to submit problems.

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I know i really liked that :(

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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.

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It usually isn't true.

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