Enhanced Sets of Hexominoes

If we take a set of hexominoes and add n copies of one of the pieces, rectangles can be made with this set for given values of n.

This can only be done for the unbalanced (by colouring) pieces and then only odd values of n are possibilities. Six of the pieces can for rectangles for all values of n. As can be seen from the diagrams below, large values of n are likely for all pieces and a complete analysis of the problem would be very time consuming.

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