Consider the hexomino depicted below (sometimes referred to as the Y6 hexomino):

+--+--+--+--+--+
|  |  |  |  |  |
+--+--+--+--+--+
   |  |
   +--+

This hexomino can tile some rectangles. The smallest rectangle is 24x23.

The hexominos in a tiling can be divided into two sets. One set will be the hexominos with their long edge parallel to the horizontal side and the other set will have their long edge parallel to the vertical side.

Prove both sets of these hexominos will have an even number of members.

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