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Problem of the Month
(July 2009)

Take a polyomino and assign a weight of 1 or 2 to each square to get a weightomino. We are interested in rectangle tilings of overlapping weightominoes so that the total weight on each square is the same. We represent these weightominoes with line diagrams, with small dots representing weight 1 and large dots representing weight 2. Note that weightominoes can be rotated and reflected, but they are not equivalent to the corresponding polycubes. What are the orders of the small weightominoes? The answers for the 2-weightominoes and 3-weightominoes are shown below.

Weightomino Order Configuration
2
2
none
2
?

Weightomino Order Configuration
2
2
4
4

Find the order of some larger weightominoes. What if weights 1, 2, and 3 are allowed?

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Problem of the Month(July 2009)

Problem of the Month
(July 2009)