ON-SETS® Variations: Senior Division

1. Multiple operations Every operation sign in Required or Permitted may be used many times in a Solution (Set-Name or Restriction or both).

2. Union and Intersection interchangeable Any Union may represent Union or Intersection, and any Intersection may represent Intersection or Union.

3. Universe and Empty Set interchangeable Any Universe may represent Universe or Empty Set, and any Empty Set may represent Empty Set or Universe.

4. Required cube The Solution must contain a ___ cube. The player selecting this variation specifies which non-digit symbol from the Resources fills the blank in the previous sentence.

5. Wild cube The ___ cube may represent any symbol on the cubes except a digit. The ___ cube must stand for the samesymbol everywhere it occurs (Restriction(s) and Set-Name). The player selecting this variation specifies which cube from the Resources is wild. The wild cube may not be a digit. Each Solution-writer must specify in writing the interpretation of the wild cube if it stands for anything other than itself in his Solution.

6. Two operations Each Solution must contain at least two operation symbols. The operation symbols are Union, Intersection, , and .

7. No Null Restrictions Each Restriction must remove at least one card from the Universe. In a chain Restriction this variation is satisfied if any part of the chain removes a card.

9. Double Color Each card in the Universe containing the ___ color will count double. The player selecting this variation specifies which one of the four colors or which one of the four color complements counts double.

10. Symmetric difference The cube means "symmetric difference;" i.e., A B equals (A B) U (B A), where these last two signs are the usual set subtraction.

11. Shift from Permitted A player may on his/her move, select a cube which has been played to Permitted and shift it from Permitted to either Required or Forbidden.

12. Blank Card Wild If the blank card has been dealt, a Solution writer must specify in writing which colors, if any, are on it. Suppose the Double Color variation is also chosen in the same Shake. Then a player choosing to put the specified color on the Blank Card makes that card count double also in that player's Solution. A player could have two copies of the same card in the Universe with this variation.

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