Discussion
The Roman senator Meritorius, his brother, his son, and his daughter have varying oratory skill levels. They are seated in rows and columns as shown in the figure with exactly one person sitting in each box. It is known that
(i) Meritorius' daughter and his brother are seated in the same column.
(ii) His son is seated diagonally across the sibling of the worst orator.
(iii) The best and worst orators are seated in the same row.
Who is the best orator?
Answer: B
The best orator is Meritorius' brother.
The sibling pairs are Meritorius and his brother, and the son and the daughter. Condition (ii) puts the son diagonally across the sibling of the worst orator.
If the worst orator were the brother, the son would sit diagonally across Meritorius, leaving the daughter and the brother in the other two boxes, which lie in different columns; this breaks (i). If the worst were Meritorius, the son sits diagonally across the brother, so the daughter must take the box in the brother's column, and Meritorius sits in the brother's row. If the worst were the son, the son sits diagonally across his sister, and by (i) the brother takes the other box in her column, which is in the son's row.
In both possible cases, (iii) puts the best orator in the worst orator's row, and that person is the brother. So Meritorius, the son and the daughter are not the best.
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