1011.1: The First-Years Dorm Solution

Congratulations to Ian Thresher '12 for winning the first logic puzzle contest of the year. Ian's name was picked at random from among the other correct entries sent in by: Jake Lucas '13, Evan Van Tassell '13, Maile Thayer '11, Brandon Wilson '14, and Walter Zonenberg '14 and Erin Luers '14. Correct entries were also submitted by Terri Smith, Betsy Bedient, and Anne Kinnel. Thanks to everyone who submitted solutions!

In our last puzzle, you were asked to determine the number of floors, and distribution of students from each of three different regions on each floor, in a new dorm, with some constraints. The Puzzler humbly begs forgiveness for his sloppiness in the original posting of the puzzle. I posted clarifications on the Logic Puzzle website on Sunday morning. I hope that no one was unreasonably befuddled.

Given the clarifications, and that each floor has to have twelve students, there are only seven possible different distributions of students on a floor, i.e. seven possible floors.

Northeast | 9 | 8 | 7 | 7 | 6 | 6 | 5 |

Rest of U.S. | 2 | 3 | 4 | 3 | 5 | 4 | 4 |

International | 1 | 1 | 1 | 2 | 1 | 2 | 3 |

Only one of the floors has more than one international student while not having four students from the rest of the United States.

Northeast | 9 | 8 | 7 | 7 |
6 | 6 | 5 |

Rest of U.S. | 2 | 3 | 4 | 3 |
5 | 4 | 4 |

International | 1 | 1 | 1 | 2 |
1 | 2 | 3 |

That leaves nineteen students from Northeast, from the twenty-six total, for the rest of the dorm, using exactly one of the columns with four students from the rest of the United States. Only one combination will work.

Northeast | 9 | 8 |
7 | 7 |
6 |
6 | 5 |

Rest of U.S. | 2 | 3 |
4 | 3 |
5 |
4 | 4 |

International | 1 | 1 |
1 | 2 |
1 |
2 | 3 |

So, the new dorm will have four floors, with the distributions highlighted above.