The heroes of AUSM try to agree on a holiday schedule. Because it’s Christmas week, everyone can email their solutions by 12:00 a.m. PST Thursday to be part of the random selection of correct answers and win a $50 gift code to ThinkGeek!
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The holiday schedule kicks in at the headquarters of the Affiliation of Unbelievably Superpowered Metahumans (AUSM). Maintenance, IT, HR, all must rearrange their work to accommodate holiday time off and such. The heroes of AUSM, Alphaman, Betadude, Gammagal, Deltakid, and Epsilonimo, realizing that evil does not take a holiday, must still hold monitor duty. However, they cannot agree on a new schedule. They come up with the following rules:
1. If Alphaman is present, Betadude must be absent unless Epsilonimo is absent, in which case Betadude must be present and Gammagal must be absent.
2. Alphaman and Gammagal may not be present together or absent together.
3. If Epsilonimo is present, Deltakid must be absent.
4. If Betadude is absent, Epsilonimo must be present unless Gammagal is present, in which case Epsilonimo must be absent and Deltakid must be present.
To be fair, the heroes have agreed that there should be a different set of heroes present at the monitors on each of the next seven days.
How do the heroes solve their problem? What should the different sets of those present and absent be while conforming to the rules they have established?
