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VTand

 Discussion on question by Sgg8: Finit…

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VTand
May 4, 2023 17:25
@Sgg8 Your new restrictions do not make the question true. Try checking with $A = \{1, 2, 3, 4\}$. There are only $6$ possible fractions in $B$: $\frac{1+2}{3+4}$, $\frac{1+3}{2+4}$, $\frac{1+4}{2+3}$, $\frac{2+3}{1+4}$, $\frac{2+4}{1+3}$, $\frac{3+4}{1+2}$. Well, actually only $5$ distinct fractions, because $\frac{1+4}{2+3} = \frac{2+3}{1+4} = 1$.
VTand
May 4, 2023 17:25
Via approach0, I found that China Team Selection Test 2014 TST 1 Day 1 Q2 (AoPS thread) asks the same question, with the added restriction "$A$ is a finite set of positive numbers".
VTand
May 4, 2023 17:25
What if $A = \{0\}$? Will we have $B = \{\}$? What about $A = \{0,1\}$ and $B = \{0,\frac{1}{2},1,2\}$?
 

 Discussion on question by Math lover …

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VTand
Feb 7, 2023 22:02
Do you know Fermat’s little theorem?
 

 Discussion on question by Firdous Ahm…

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VTand
Jan 29, 2022 10:34
Suppose $a_{ij} = 1$. By the first condition, $a_{ij} = 1$ implies $a_{ji} = 0$. But if $a_{ji} = 0$, then $a_{ij} = 0$ due to the second condition. Is there something wrong with the conditions?
VTand
Jan 29, 2022 10:34
This seems similar to your previous question, although presented in a different way? We have $a_{ij} = 1$ iff $(i, j) \in R$.
 

 Discussion between soupless and Marcu…

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VTand
Dec 3, 2021 17:49
Well, there isn't one, because "close" is vague.
Here's another scenario: Consider the points $(-10, 0)$, $(10, 0)$ and $(x, 0)$ for some $-10 < x < 10$. The smallest circle to contain all three points is the circle of radius $10$ centred at $(0, 0)$, regardless of the exact value of $x$. Yet, your algorithm would change the radius and the centre depending on the value of $x$.
VTand
Dec 2, 2021 12:51
@soupless How does the algorithm define which points are close and which are not?
 

 Discussion on question by PtF: Maximi…

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VTand
Nov 21, 2021 14:41
@SakethMalyala The options are from A to E. Perhaps you meant 8 questions for A&B, and 4 question each for A&C, A&D, and A&E.
VTand
Nov 21, 2021 14:41
@PtF This is a minor issue, but question 14 in the image only has one selected option.