106 circles can fit in a 10x10 square.
8 rows of row/column packed circles (which take up 8 units of space) can be replaced by 9 hexagonally packed rows (which take up 1+8*sqrt(3)/2 = 7.928 units of space.) This leaves 2 more units of space in the square which can be filled with two complete rows of 10 circles. Altogether, there are 4 rows with 9 circles and 7 rows with 10 circles. |