1998 Pascal Problem 25

One way to pack a 100 by 100 square with 10\,000 circles, each of diameter 1, is to put them in 100 rows with 100 circles in each row. If the circles are repacked so that the centres of any three tangent circles form an equilateral triangle, what is the maximum number of additional circles that can be packed?

\textbf{(A)}\ 647\quad \textbf{(B)}\ 1442\quad \textbf{(C)}\ 1343\quad \textbf{(D)}\ 1443\quad \textbf{(E)}\ 1344

If there are no answer choices shown, enter a numerical answer.

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