Birthday collision: On planet X, there are 256 days in a year. One person enters a room, one at a time. Each person has equal chance to be born on any day of the year. Close the door when the last person entering shares the same birthday with someone else in the room. Count the number of people in the room. Repeat 1000 times.
This is one of the statistical tests for randomness (D. Heath and P. Sanchez, 1986). If there are correlations between numbers, then we would expect a skewed outcome.

N2--1112--2122--3132--4142--5152--6162--7172--8182--9192--101102--111112--257
# times there were N people