A little while back, the incredible 3blue1brown started
posting
monthly math problems. This recent
one was
particularly engaging for me,
and after solving it using pigeonhole principle, I started wondering what the expected number of pairs was,
rather than the
pigeon-holed minimum. Wrote this monte carlo simulation to validate my answer. (spoiler: either I, or the
sim (or both (woah triple nested parentheses!)) was wrong)
The sim comes out to about 10.66 expected pairs.