Needle on a Grid
A floor is ruled into unit squares by two families of parallel lines (a square grid with spacing 1). A needle of length 1 is dropped at random: its centre is uniform over a tile and its direction is uniform, independent of the centre. What is the probability that the needle crosses at least one grid line? Give an exact closed form, or a decimal rounded to 4 places.
Related problems & prerequisites
Worth solving first
- One Point per Side 3.0/10
- Ten Letters, Ten Envelopes 3.0/10
- Monochromatic Triangles 2.0/10
Source: The Buffon-Laplace needle problem (Laplace, 1812). Statement written for AxiomIQ.