The way the distribution worked was that a small cabinet used to be replenished by some 50 odd t-shirts at some random time in the week. Those who wanted a t-shirt (definitely all interns, but not sure if it was limited to them alone. More on this shortly) ran a manual poll or a select loop on that cabinet. If the word spread that the cabinet has been replenished there would a mad rush. It was not that the t-shirts were like no other, but the artificial scarcity made it fun to get one. We interns definitely fought for it like a trophy. The more prized ones were the Ts for women. Good gift for your girlfriend. My personal favorite was the Wienberger T. It was not Googly enough to attract unwarranted attention.
The vibe the t-sirts created was quite opposite of "here we all wear Google Ts". It was more like, "I got one and you didn't", a fun competition to humor each other with.
Soon some Googler figured out that one could set up a webcam to monitor that cabinet. The ip address of that cam was publicly distributed. I suspect a fair number of people really wanted these t-shirts because the cam would always clog up on the traffic, to the point of being almost useless. That's a shame because someone wrote an application to compare consecutive frames from that cam so that it will send out a message once it detected a change. Its a bit tricky, you do not want it to trigger whenever someone walked passed that cabinet. Particularly so because it was right on the way to the cafeteria. So one had to average out the frames so that any change that persisted roughly for the amount of time that is required to stuff the cabinet triggered the system but not others. A low-pass filter for t-shirt stuffing.
Not sure if anyone wrote a predictive model to figure out when that t-shirt cabinet will be stuffed. But I would not be surprised if anyone did. The culture inside seemed just right for these kind of things.