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Throw a cubical die into the air, and photograph it with a high-speed camera in midflight. Assuming half the faces are visible in each photo, what is the *average* number of times you would need to throw-and-photograph the die before all 6 faces have been photographed?
[This is inspired by a similar puzzle for a sphere, https://twitter.com/mikeandallie/status/1663710291769557002, for which Mike Lawler and Christopher Long found a very nice solution for any dimension.]
TwitterMike Lawler on Twitter“1/6 or so. This is a problem I had fun playing around with today. I don't know how to solve the ball problem, yet, but I did find a solution to the problem with a circle instead of a ball.”
