Problem 653

[Wizard_Montly]

I've gotten into a bit of a rut were I wouldn't have thought i would.

on Problem 653 (View Problem) the particles's positions are given in millimetres but more importantly, integer values. My problem that I've realised that if two particles were to move toward each other while they are an odd number of millimetres away, they would meet at a point with half-integer position ( with a .5); which seemingly goes against what the rest of the problem is implying i.e that all values are integer, including the answers.

can someone please confirm if I'm overthinking this or if its as simple as the final answer does not have any fractional element regardless.

[RobertStanforth]

My problem that I've realised that if two particles were to move toward each other while they are an odd number of millimetres away, they would meet at a point with half-integer position ( with a .5); which seemingly goes against what the rest of the problem is implying i.e that all values are integer, including the answers.

You are correct that marbles can meet at half-integer positions.
The results (distances travelled) given in the test cases are all integers. I can clarify that they are exact - they have not been rounded.
As for whether that is true in general for all starting configurations: that question should be settled while you solve the problem.

[Wizard_Montly]

Thank you for clarifying, very appreciated.