Question

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?

	Column 1	Column 2
Row 1
Row 2

• A. Meritorius
• B. Meritorius' brother
• C. Meritorius' son
• D. Meritorius' daughter

Hint:

Fix the daughter and brother in one column using clue (i), then use the diagonal-seat clue (ii) to find who is the worst orator before applying the same-row clue (iii).

Answer 1

The Correct Option is B

Step 1: Set up the family relations.
There are four people: Meritorius (M), his brother (Br), his son (S), and his daughter (D). M and Br are siblings of each other. S and D are siblings of each other, both children of M.

Step 2: Use clue (i) to fix the columns.
Clue (i) puts the daughter and the brother in the same column. Since each column has exactly two boxes, D and Br occupy the two rows of one column, in some order. This leaves the other column for M and S, one in each row.

Step 3: Use clue (ii) to find the worst orator.
The son sits diagonally across from "the sibling of the worst orator". A diagonal seat lies in the opposite row and the opposite column. Since the son sits in the M/S column, the diagonal seat lies in the D/Br column, in the row opposite to the son's row. So either D or Br sits there and is the sibling of the worst orator. If D sits there, D's only sibling is the son, so the son is the worst orator. If Br sits there, Br's only sibling is Meritorius, so Meritorius is the worst orator.

Step 4: Check the first case with clue (iii).
Here the worst orator is the son, and the daughter sits diagonally opposite him, so she is not in his row. The son's row must then hold the son and the brother. By clue (iii), the best orator shares the worst orator's row, so the best orator in {son, brother} must be the brother.

Step 5: Check the second case with clue (iii).
Here the worst orator is Meritorius, and the brother sits diagonally opposite the son, so the daughter shares the son's row. Meritorius then sits in the row that also holds the brother. By clue (iii), the best orator must share Meritorius' row, so the best orator in {Meritorius, brother} must be the brother.

Step 6: Final conclusion.
Both possible arrangements point to the same person as the best orator.
\[ \boxed{\text{Meritorius' brother}} \]