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The brother of a classmate, who is in elementary school, got the following homework, but he can't figure it out. So his brother shared it to see if someone in his class could help out with it:

"Write the number 1000 with 3 numbers 13". Only the standard arithmetic operations of addition, subtraction, multiplication, and division are allowed.

How does one solve this problem?

user64742
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freethinker36
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    Try https://puzzling.stackexchange.com/ instead – thedumbkid Sep 29 '20 at 22:01
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    Are you permitted to use the floor and square root functions? What is $\lfloor \sqrt{13}\rfloor$? – user2661923 Sep 29 '20 at 22:05
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    I agree with @AnanyapamDe . Also, this needs more details - e.g. what operations are allowed? – Vepir Sep 29 '20 at 22:22
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    @user64742: A statement can be a perfectly good question: "Compute the square root of 11." "Find the inverse of $f(x) = \sin x$." "Find the smallest prime factor of 3985984509845." All perfectly acceptable on this site, including "Write the number $1000$ with $3$ numbers $13$." (+1... to counter your -1) – David G. Stork Sep 29 '20 at 22:27
  • @David, if someone posted "Compute the square root of $11$" as a question on this site, it would be closed in a flash. – Gerry Myerson Sep 29 '20 at 22:32
  • $13+13+13+961$. (Well, it said to use "three numbers 13", it didn't say you couldn't use some other numbers, too.) – Gerry Myerson Sep 29 '20 at 22:34
  • @GerryMyerson: Geez... You simply do not see the principle behind the comment. You need an example all spelled out... OK: "Given a directed Erdos graph of size $V=39$ and $p = .4$, compute the probability there is a Hamiltonian path." (What!!... no question!!!). Would that be "closed in a flash"?! Do you see the principle yet? – David G. Stork Sep 29 '20 at 22:35
  • @David, that one would probably be closed pretty quickly, too, for "lack of context". Why don't you try posting it, and see? – Gerry Myerson Sep 29 '20 at 22:38
  • @GerryMyerson: Oh really geez... a comment doesn't have room for the full context, such as appears in this question. I could easily post my "statement-question" with context (a diversionary irrelevancy) but I don't need to: Here are unclosed questions (with answers and upvotes) that consist of only statements, the issue at hand: https://math.stackexchange.com/questions/3844314/connected-components-of-a-coset-space https://math.stackexchange.com/questions/3845520/the-length-approximately-equals-width-the-length-is-three-times-the-height-the etc. – David G. Stork Sep 29 '20 at 22:43
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    The question still remains, what operations/functions are allowed. One could do this using a single $13$ very simply... such as $f(13)=1000$ where $f$ is a constant function mapping everything to $1000$. Or, if you want it to be a well known named function, how about $\underbrace{S(S(S(\cdots (13)\cdots )))}_{986~\text{copies of S}}=1000$ where $S$ is the successor function, the most fundamental of all functions upon which all other operations on numbers in peano arithmetic build from. If these are not allowed, despite their simplicity, then it must be clarified what is allowed. – JMoravitz Sep 29 '20 at 22:55
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    "you have failed to miss my point." I simply don't know how to respond to that. – David G. Stork Sep 30 '20 at 06:00
  • Hey everyone. With all these comments it is evident that the teacher failed in providing a clear problem to solve to an ELEMENTARY school student! – freethinker36 Oct 06 '20 at 23:36
  • @user64742 You are mistaken. I presented the problem as the teacher presented it. I presented another problem that was solved as context. But regarding what the teacher was teaching, I was not supplied with that information. – freethinker36 Oct 31 '20 at 00:21

3 Answers3

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If you can break up the $13$'s: $(13-1\times 3)^{1\times3} = 1000$.

Robert Israel
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    Well... I strongly doubt one can break up the digits in this way... but admittedly that is not clear from the question. Are we allowed to write $1313$, then? or $131 \times 3$? or... – David G. Stork Sep 29 '20 at 22:32
  • Alternatively, $3=1\times 3=\lfloor \sqrt{13}\rfloor$ as already suggested in the comments. – Vepir Sep 29 '20 at 22:43
  • @Vepir: Exactly, and the OP certainly has not signed off on $1 \times 3$ (for example), so apparently nobody knows (still). – David G. Stork Sep 29 '20 at 22:49
  • I also remembered, $3=\lfloor\lg13\rfloor$ too, where $\lg$ is the binary logarithm. – Vepir Sep 29 '20 at 23:16
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I wasn't going to answer, because I agree with Ananyapam De's comment that this is the wrong site. However, from all of the reactions...

$\left(13 - \lfloor \sqrt{13} \rfloor \right)^{\lfloor \sqrt{13} \rfloor}.$

user2661923
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-1

Is this allowed ?

$$(1(13-13))^3=(10)^3$$

hamam_Abdallah
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