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You can fit a maximum of 36 blocks.

This is because the blocks can fit evenly by length and width (2 x 3 x 6 = 36) or 6 levels of 6 blocks each.

You can verify this by dividing the volume of the box (6 x 6 x 6 = 216 cu in) by the volume of a block (3 x 2 x 1 = 6 cu in). 216/6 = 36

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