The Largest JC-Made Hall of Mirrors Lying on Southern Colby Campus
By Asilata Bapat and Don Laackman
Answer: CETACEAN
This is a liars/truthtellers logic puzzle combined with a mirror hall puzzle. Here is the sequence of deductions. One cannot get very far by looking just at the statements or just at the halls; both sets of data need to be used.
- David must be lying: there is no way for him to see Yuval in the first hall since only one mirror is added.
- We now know that David was always standing next to a mirror. We use this to mark off mirror positions: Row 1/Column 1 in Hall 1, Row 3/Column 1 in Hall 2, Row 1/Column 5 in Hall 4, Row 3/Column 5 in Hall 6, and Row 1/Column 2 in Hall 7.
- Some pairs of JCs have contradicting statements (not both can be true): David and Sonya, Jeff and Yuval, Jeff and Kristin, Mia and Sachi, Sachi and YQ, Sachi and Yuval.
- Some pairs of JCs have corroborating statements (one is true if and only if the other is true): Kristin and Mia, Sonya and YQ.
- Sonya's and David's statements actually contradict each other, so Sonya is telling the truth.
- Since YQ's statement agrees with Sonya's, YQ is also telling the truth.
- Hence Sachi is lying.
- In Hall 3, there has to be a mirror along Jeff's line of sight and also along Sachi's line of sight, and we have all mirrors but one, so there's a mirror at the intersection of the two. We also know its orientation because Jeff has to be able to see someone.
- Mia has to be able to see someone in Hall 2, and that gives us the orientation of the mirror at Row 1/Column 1.
- This means that Sonya and David can see each other in Hall 1. Since Sonya is telling the truth, we deduce the orientation of the mirror at Row 3/Column 1 of Hall 2, and at Row 1/Column 5 in Hall 4.
- Since Sonya and David do not see each other in Hall 6 either, we can deduce the orientation of the mirror at Row 3/Column 5. (If there were another mirror along that path, Sonya wouldn't be able to see anybody.)
- Mia sees Yuval in Hall 5. So she is telling the truth. Hence Kristin is also telling the truth.
- By Kristin's statement, we have a mirror in Row 5/Column 1 in Hall 5, so that she sees YQ.
- Since Kristin sees YQ three times, the only other possibility is Hall 8. This gives us the mirror in Row 2/Column 2 of Hall 8.
- Now we have all mirrors, so we go back to each JC's statement to find the status of all remaining JCs. We find that Mia, Kristin, YQ and Sonya are the only truthtellers.
The solved mirror puzzles and the lines of sight of the truthtellers are shown below:
These spell the answer, CETACEAN.
