### BeeTLE's blog

By BeeTLE, history, 4 weeks ago, ,

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)

• -16

 » 4 weeks ago, # |   0 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 ).
•  » » 4 weeks ago, # ^ |   0 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 $t = 1$.
•  » » » 4 weeks ago, # ^ |   0 Thanks for explanation...I just needed to know if they are asking answer possibly on different time.