The Parking Constant
Cars of length 1 arrive one at a time at a kerb of length L. Each car parks in a position chosen uniformly at random among all positions where it fits without overlapping a previously parked car (and stays inside the kerb). This continues until no gap of length at least 1 remains. As L → ∞, the expected fraction of the kerb covered by cars tends to a constant. Give that constant rounded to 3 decimal places.
Related problems & prerequisites
Worth solving first
- Break the Longer Piece 6.0/10
- Real Roots at Random 6.0/10
- Square Beats Product 5.0/10
Source: Rényi's parking problem (Alfréd Rényi, 1958). Statement written for AxiomIQ.