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)

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

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`\boxed{123}`

## 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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