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.

#Math #Opinions

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Your statement is not necessarily true.

Calvin Lin Staff - 7 years, 7 months ago

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

Daniel Chiu - 7 years, 7 months ago

thats a good idea

Tyler Gold - 7 years, 7 months ago

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 - 7 years, 7 months ago

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 - 7 years, 7 months ago

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 - 7 years, 7 months ago

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 - 7 years, 7 months ago

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

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

Cole Coupland - 7 years, 7 months ago

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

Selene (Elly) Kirkland - 7 years, 7 months ago

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

Taehyung Kim - 7 years, 7 months ago

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

john bakradze - 7 years, 7 months ago

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

Ryan Soedjak - 7 years, 7 months ago

I know i really liked that :(

Tyler Gold - 7 years, 7 months ago

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 - 7 years, 7 months ago

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

It usually isn't true.

Ryan Soedjak - 7 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$