1314.1: Logic Roommates - Solution

 

In our first puzzle of the year, you were given some test scores among three pairs of roommates and asked to identify the three pairs. Ashleigh had a 96, Belinda had a 92, Camille had a 90, and Debra had an 84. Edna and Farah had 88 and 86, but we did not know which student had which score. Two pairs of roommates had the same total grades. Camille lives in South. Belinda lives in Babbitt. Debra’s roommate had a lower grade than Edna’s roommate.

 

The Winner

Congratulations to Kerkira Stockton ‘14 for winning the logic puzzle. Kerkira’s name was drawn at random from the twenty-one different successful solutions submitted by her and Milinda Ajawara 16, Erin Bernard ‘16, Josh DeVinney ‘15, Sarah Dimakis ‘17, Leigh Gialanella ‘15, Edward Hincks ‘15, Lauren Lanzotti ‘14, Spencer Livingstone ‘16, Ben Moody ‘15, Megan Murphy 15, Juliana Newman ‘17, Amy Resnik ‘15, Sunrose Shrestha ‘14, Becca Straw ‘14, Andrew Szatkowski ‘15, Tsion Tesfaye ‘16, Reina Weinstock ‘17, Brandon Wilson ‘14, Mandy Wong ‘15, and Sharon Yam ‘16. Other well-explained solutions were submitted by Dick Bedient (Mathematics), John Murphy (C&D), and Boriana Pratt (Economics). Even more solutions were submitted, but the puzzler has to keep high standard for explanation; after all, we are a writing college!

 

The Puzzler's Solution

I saw two successful approaches among the solutions submitted. One approach started by using the given constraints to find roommate pairs. I started by looking for matching pairs of score sums.


I first calculated the total grade for all possible pairs. Since there were six students, there were only 6C2, or 15, combinations. Of these, there were five sets of duplicate totals.

 

Total Grade Pair 1 Pair 2 Remaining Pair (Total)
174 C and D 86 and 88 A and B (178)
176 B and D C and 86 A and 88 (184)
178 B and 86 C and 88 A and D (180)
180 A and D B and 88 C and 86 (176)
182 B and C A and 86 D and 88 (172)


The 174 solution is out because Debra’s roommate is supposed to have a lower grade than Edna’s. (We don’t know whether Edna has the 88 or the 86 at this point, but it doesn’t matter because Debra’s roommate has 90 on the 174 solution.) Ditto for the 178 and 180 solutions, where Debra’s roommate has the highest score. That leaves the 176 solution and the 182 solution. But the 182 solution is out because Belinda and Camille live in different dorms. So the 176 solution is right.


So Belinda and Debra live together. But we still don’t know which grade is Edna’s and which grade is Farah’s, and consequently who their roommates are. If Edna got the 86, then her roommate’s score (90) would be lower than Debra’s roommate’s score (92). So Edna got the 88 and rooms with Ashleigh while Farah got the 86 and rooms with Camille.

 


Prizes

 

Prize winners receive a t-shirt or mug from Lulasail, home of the best philosophy t-shirts on the web.