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An uncertain number of people sit in a row facing north. Only two people are between T and the person who likes Pink. M is three places away from the person who likes Grey. As many people are between J and X as between S and the person who likes Yellow. The person who likes Green is fifth to the left of Y. Q is four places away from the person who likes Grey. R is second to the left of the person who likes Black. Nine people are between B and the person who likes Pink. J is seventh from the right end. No one is to the left of the person who likes Red. S is to the right of J. Three people are between the person who likes Blue and J. Neither B nor X likes Violet or Yellow. As many people are between Y and S as between the person who likes Red and T. The person who likes White is two places away from J. The person who likes Blue is fifth to the right of B. T is fourth to the right of the person who likes Black. R is two places away from Q. Q is fourth from the left end. No one is to the left of R. The number of people between Q and T is one less than the number of people between B and Y. J is not next to the person who likes Blue. More than six people are between Y and the person who likes Pink. More than six people are between M and the person who likes Green. M is not to the left of T. What is the strength of the row?
- 30
- 46
- 39
- 36
Correct answer: 36
Solution
This is a complex linear arrangement with multiple positional constraints. By anchoring Q at the fourth position from the left, R at the leftmost side, and J seventh from the right, the remaining conditions on relative distances and color preferences force a unique arrangement. The total number of seats comes out to 36.
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