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:

Clue (i) forces the daughter and brother into one column and Meritorius plus the son into the other; then work out who clue (ii) allows the worst orator to be.

Answer 1

The Correct Option is B

Step 1: List the four people and their sibling pairs.
The four people are Meritorius (M), his brother (Br), his son (S), and his daughter (D). There are two sibling pairs here: M and Br are siblings of each other, and S and D are siblings of each other. This matters because clue (ii) talks about the sibling of the worst orator.

Step 2: Use clue (i) to fix the column structure.
Clue (i) says D and Br sit in the same column. In a 2 by 2 grid, two people in the same column occupy Row 1 and Row 2 of that column, one below the other, so they are never diagonal to each other. Since the grid has only 4 seats and D, Br fill one full column, the remaining column must be filled entirely by the other two people, M and S. So M and S also share the other column.

Step 3: Use clue (ii) to narrow down who the worst orator can be.
Clue (ii) says S sits diagonally across from the sibling of the worst orator. Since S sits in one column (with M), S's diagonal partner sits in the other column, the one holding D and Br. So the sibling of the worst orator must be D or Br. If that sibling is Br, the worst orator is M. If that sibling is D, the worst orator is S. The sibling cannot be M or S themselves, since M and S sit in the other column and cannot be diagonal to S. So the worst orator is either M or S, never Br or D.

Step 4: Work out the grid for the case worst orator equals M.
Here the sibling of the worst orator is Br, so clue (ii) needs Br diagonal to S. Say Br sits at Row 1 Column 1; its diagonal seat is Row 2 Column 2, so S sits there, which forces M to Row 1 Column 2 and D to Row 2 Column 1. The seating becomes: Row 1 has Br and M; Row 2 has D and S. By clue (iii), the best and worst orator sit in the same row. Worst orator M sits in Row 1, so the best orator is the other person in Row 1, which is Br.

Step 5: Check the other case, worst orator equals S, to confirm the answer does not change.
Here the sibling of the worst orator is D, so clue (ii) needs D diagonal to S. Placing S at Row 1 Column 2, its diagonal is Row 2 Column 1, so D sits there, forcing Br to Row 1 Column 1 and M to Row 2 Column 2. The seating becomes: Row 1 has Br and S; Row 2 has D and M. Worst orator S sits in Row 1, so by clue (iii) the best orator is the other person in Row 1, which is again Br.

Final Answer:
Both logically valid cases point to the same person for the best orator. \[ \boxed{\text{Meritorius' brother}} \]