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By BeeTLE, history, 4 weeks ago, In English,

In PROBLEM F,1311F Can anybody explain at what point below coordinates coincide?

3
1 5 10
9 6 1

A B C (suppose names of points)

Ans is 0 I guess. But I don't understand at which point? (maybe I'm assuming something wrong)

At 1 sec: A = 10, B = 11, C = 11 (Only d(B,C)=0)

At 1.x sec:

A = 11.a, C = 11.a, B = 11.b where b>a ( only d(A,C)=0)

At 1.y sec: (y>x)

C = 11.c, A = 11.d, B = 11.d where b>a (only d(A,B)=0)

At 1.z sec: (z>y)

C = e, B = f, A = g where g>f>e (diff increases more hereafter)

 
 
 
 
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4 weeks ago, # |
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I agree that the question was not well framed. It could have been explained better.

What the question is saying is, $$$ d(i,j) $$$ is smallest distance between points $$$i$$$ and $$$j$$$ over all time $$$ t $$$. And you need to find $$$ \sum\limits_{i,j}{d(i,j)} $$$. They are not asking $$$ \sum\limits_{i,j}{d(i,j)} $$$ at a particular time. Basically, $$$ d(0,1) $$$ might be minimum at time $$$ t = 1 $$$, and $$$ d(1,2) $$$ might be minimum at time $$$ t = 4 $$$, and you just have to tell sum of these smallest possible distances between each pair of points ( at any time, independent of each other ).

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    4 weeks ago, # ^ |
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    To explain the example that you have given,

    Points $$$A$$$ and $$$B$$$ have $$$ d(A,B) = 0 $$$, because there is a time $$$ t = \dfrac{4}{3} $$$ such that, $$$ x_A = x_B = 13 $$$.

    Points $$$A$$$ and $$$C$$$ have $$$ d(A,C) = 0 $$$ because they intersect at time $$$ t = \dfrac{9}{8} $$$.

    And, finally, Points $$$B$$$ and $$$C$$$ also have $$$ d(B,C) = 0 $$$ because they intersect at time $$$ t = 1 $$$.

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      4 weeks ago, # ^ |
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      Thanks for explanation...I just needed to know if they are asking answer possibly on different time.