Picture Board

Puzzle: A company keeps two corkboards in the lobby on which they pin Polaroids of new employees on their first day. The pictures are ordered by start date of the employee, putting the most senior employee in the upper-left of the first corkboard, filling it up, and then starting on the second corkboard. When employees quit, their pictures are removed and everyone else’s pictures shift over.

You just started at this company and desperately want to see your picture move onto the first corkboard, where you will get prestige as an old-timer. You estimate that one person starts per week and one person quits per week. There are 150 pictures per board. Both boards were full when you started. How long will you have to wait on average to get onto the first board?

(This puzzle was originally written by Grue.)

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