MathDB

Initially, the point-like particles

A, B

and

C{}

are located respectively at the points

(0,0), (1,0)

and

(0,1)

in the coordinate plane. Every minute some two particles repel each other along the straight line connecting their current positions, moving the same (positive) distance.
[*]Can the particle

A{}

be at the point

(3,3)

? What about the point

(2,3)

? [*]Can the particles

B{}

and

C{}

be at the same time at the points

(0,100)

and

(100,0)

respectively?
Proposed by K. Krivosheev

Problem Statement