Packing problems of this kind are obviously equivalent to the problems of placing k (here 9) points in a unit square such that the minimum distance between any two of them be as large as possible. The solutions of these problems are known for 2 ≤ k ≤ 9. The largest possible minimum distances m k are given in table 1, and the corresponding "best" configurations shown in figure 1.
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J. Schaer (1965) studied this question.