1011.4: Four Students Solution
Congratulations to Adam Fix '13 for winning the Fourth Logic Puzzle Contest! Adam’s name was chosen at random from the submissions by Hamilton students with correct solutions.
Other correct solutions were submitted by Will Boudreau '14, Peter Cragnoline '13, Beril Esen '13, Catherine Gold '14, Duo Gong '14, Jess Gutfleish '14, Andrew Harris '11, Kathleen Herlihy '14, Alex Host '13, Jack Kissel '13, Lauren Lanzotti '14, Joe Legault '14, Tongxin Lu '11, Leeds Pierce '12, Sunrose Shrestha '14, Rachel Slivken '13, Jackie Specht '12, Maile Thayer '11, Ian Thresher '12, Brittany Tomkin '12, and Walter Zonenberg '14; The Bedient Family, Joy Simon, and Simon Stanco also sent in correct solutions.
You were asked to assign four students (Bobby Babbitt, Connie Carnegie, Millie Minor, and Ned North) to the four dorms which share their names, knowing that none of them live in the dorm that shares his or her name. Further, you were given five statements, only one of which was true.
1. Millie Minor lives in Babbitt.
2. The person who lives in Carnegie is neither Bobbie Babbitt nor Millie Minor.
3. Ned North lives in Minor.
4. Neither Connie Carnegie nor Bobby Babbitt lives in North.
5. Connie Carnegie lives in Babbitt.
We have to find the true statement, using reductio ad absurdum arguments. In reductio arguments, you assume the opposite of what you wish to prove. When you derive a contradiction, you have shown that your assumption is false.
To solve our puzzle, we will assume, in turn, that each of the premises is true. When we find that one premise’s truth entails the truth of another premise, we will have found a contradiction with the claim that only one of the premises is true, and we can reject our assumption. Only one assumption will avoid contradiction.
Note that since there are four students assigned to four dorms, there must be one student in each dorm.
Suppose that 1 is the true statement. Then, Millie Minor would live in Babbitt. Since Ned North could not live in North, Babbitt (since Millie Minor would), or Minor (since 3 would have to be false), he would have to live in Carnegie. But now 2 would be true. So, 1 is false.
Suppose that 2 is true. Then, Ned North would live in Carnegie. Millie Minor could not live in Babbitt (from 1), or Minor or Carnegie. So, she would live in North. That would make 4 true. So, 2 is false.
Suppose that 3 is true and Ned North lives in Minor. Then 1 would be false and Millie Minor would not live in Babbitt. So, Connie Carnegie would live in Babbitt and 5 would be true. So, 3 is false.
Suppose that 5 is true and Connie Carnegie lives in Babbitt. Bobbie Babbitt would live in North, from 4. Ned North thus could not live in Babbitt or Carnegie, and he could not live in North. So, 3 would be true. So, 5 is false.
Thus, 4 is true. Millie Minor lives in North, contradicting 1. Bobbie Babbitt lives in Carnegie, from 2. Ned North lives in Babbitt, from 3. And Connie Carnegie lives in Minor, which contradicts 5.