An insect starts at the point (0, 0) on the Cartesian plane, and each minute jumps exactly 1 unit to a point having rational coordinates.

(i) Describe the procedure whereby the insect will be able to reach the point (1/5, 1/17) in a finite amount of time.

(ii) Can the insect ever reach the point (0, 1/4)? Provide adequate reasoning for your answer.

I think this page is the source of the puzzle:

Posted by Brian Smith on 2016-10-30 18:25:24