1011.1: The First-Years Dorm
Hamilton College is planning to build a new dormitory for first-year students. Each floor of the new dorm will house twelve students. The dormitory will integrate students coming from three different regions: the Northeast, the rest of the United States, and other countries. Each floor will have more students from the Northeast than from the rest of the United States, and more students from the rest of the United States than from other countries. Also, each floor will have a different distribution of students from the different regions. Altogether in the dorm, there will be twenty-six students from the Northeast. One floor will have four students from the rest of the United States, and a different floor will have more than one international student.
Clarifications: Each floor must have at least one student from each of the three regions: Northeast, the rest of the United States, and other countries. Exactly (not at least) one floor has four students from the rest of the United States.
How many floors will the new dorm have?
What will be the distributions of students on each floor?
Explain your solutions.
Solutions, with explanations, to Puzzle #1011.1: The First-Years Dorm may be sent to email@example.com, or, via campus mail, to Russell Marcus, Philosophy Department. Make sure to include your contact information with your solution. A winner will be chosen among those who submit satisfactory solutions. Any one may play the puzzle, but only current Hamilton College students may win prizes.
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