1314.2: Four Students, Four Courses - Solution
Congratulations to Sunrose Shrestha ‘14 for winning logic puzzle contest 1314.2! The Puzzler was especially pleased that Sunrose’s name came out of the hat since he has been a stalwart puzzle solver for years and submitted an excellent clear and detailed solution! Others who submitted correct and well-explained solutions are: Milinda Ajawara ‘16, Sarah Andrews ‘14, Jennifer Baxter ‘14, Katie Bor ‘16, Brisa Camacho-Lovell ‘16, Robert Clayton ‘15, Josh Devinney ‘15, Sean Fujimori 14, Tori Fukumitsu ‘15, Luke Gernert ‘16, Duo Gong ‘14, Jordan Graziadei ‘15, Jess Gutfleish ‘14, Ja Hsien Ho ‘15, Lauren Lanzotti ‘14, Spencer Livingstone ‘16, Emily Moschovits ‘17, Vineeth Rao ‘15, Brandon Wilson ‘14, and Sharon Yam ‘16.
You were asked to determine which two of four popular courses (Biology 101, Chemistry 120, Physics 101, and Sociology 101) each of four students took. No two of the students had the same two courses and no course was taken by all four students; only one of the four courses was taken by three of the students. No one took both chemistry and physics. Barbara didn't take biology. Celarent took physics and had one course with Ferio, but didn't take a course with Darius. Barbara, Darius, and Ferio did not all have a course together, but Celarent and Darius each took a course with Barbara.
The Puzzler's Solution
Since Barbara didn't take biology, she must have taken sociology and either physics or chemistry. Since Celarent took physics, her second course has to be either sociology or biology. Since Celarent had no course with Darius, Darius must have taken whichever of sociology or biology that Celarent did not take and chemistry.
Barbara Celarent Darius Ferio Sociology Physics Chemistry Phy/Chem Soc/Bio Soc/Bio
Since Celarent and Darius each took a course with Barbara, there are only two ways to finish the first three columns of the second row of the above table. If Barbara took physics, then Darius took sociology with her and Celarent took biology. If Barbara took chemistry, then Celarent took sociology with her and Darius took biology. Let's call these two ways of completing the first three columns of the table Option A and Option B.
Barbara Celarent Darius Ferio Sociology Physics Chemistry Physics Biology Sociology
Barbara Celarent Darius Ferio Sociology Physics Chemistry Chemistry Sociology Biology
In Option A, Ferio can't take sociology since he didn't have a course with Barbara and Darius. So he had to take two of physics, biology, and chemistry and he couldn't take both physics and chemistry. So Ferio took biology. With seven of the eight courses determined, we have two students in physics, sociology, and biology and one student in chemistry. Since one of the four courses was taken by three of the students, Ferio's second course has to be physics. But then Ferio's schedule would be identical to that of Celarent, which contradicts the given information. So Option A is impossible.
Of the six courses already determined in Option B, two students took chemistry and sociology and one student took biology and physics. Ferio couldn't have taken Chemistry because he didn't have a course with Barbara and Darius. Since one course was taken by three students, Ferio must have taken sociology. This leaves either physics or biology for Ferio's second course. But if Ferio took physics, he would have had the same schedule as Celarent.
Barbara Celarent Darius Ferio Sociology Physics Chemistry Sociology Chemistry Sociology Biology Biology
One more thing
The Puzzler was struck by the fact that no one mentioned the source of the four students’ names. I thought of running a contest to see who could figure it out first, but it’s just too easy to determine by Googling. If you don’t know already, I suggest you find out (especially students of logic)!
Prize winners receive a t-shirt or mug from Lulasail, home of the best philosophy t-shirts on the web.