perplexus.info :: Probability : An Infinite Lattice of Points

An Infinite Lattice of Points (Posted on 2024-05-23)

Consider an infinite square lattice of points with integer coordinates on a plane.

If two lattice points are chosen at random, what is the probability that the straight-line segment joining the two lattice points will not pass through any other lattice points?

**** Adapted from a problem appearing in the 2005 Fall collection of BENT, Brain Ticklers.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The required probability is ~6/π² =~ 0.607927101854027.
For an explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution via Euler	Brian Smith	2024-05-24 11:19:35
solution -- simulation and research	Charlie	2024-05-23 12:23:44

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