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Some empirical data, with each point the average of 50 trials:
           MinDistSquare http://cs.smith.edu/~orourke/MathOverflow/MinDistSquare.jpg
The curve $1/(\sqrt{2} n)$ (displayed) fits rather well. Congrats to Douglas Zare and Ori Gurel-Gurevich!

Some empirical data, with each point the average of 50 trials:
          
The curve $1/(\sqrt{2} n)$ (displayed) fits rather well. Congrats to Douglas Zare and Ori Gurel-Gurevich!

Some empirical data, with each point the average of 50 trials:
           MinDistSquare http://cs.smith.edu/~orourke/MathOverflow/MinDistSquare.jpg
The curve $1/(\sqrt{2} n)$ fits rather well. Congrats to Douglas Zare and Ori Gurel-Gurevich!

Some empirical data, with each point the average of 50 trials:
           MinDistSquare http://cs.smith.edu/~orourke/MathOverflow/MinDistSquare.jpg
The curve $1/(\sqrt{2} n)$ (displayed) fits rather well. Congrats to Douglas Zare and Ori Gurel-Gurevich!

Some empirical data, with each point the average of 50 trials:
           MinDistSquare http://cs.smith.edu/~orourke/MathOverflow/MinDistSquare.jpg
The curve is $1/(\sqrt{2} n)$.

Some empirical data, with each point the average of 50 trials:
           MinDistSquare http://cs.smith.edu/~orourke/MathOverflow/MinDistSquare.jpg
The curve $1/(\sqrt{2} n)$ fits rather well. Congrats to Douglas Zare and Ori Gurel-Gurevich!