ON-SETS® Variations: Middle 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.

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