Seven friends, Abe, Bob, Chad, Dolly, Elisa, Frank, and Gregory sit in a VIP enclosure of a stadium to watch a football match. The seats in the enclosure form a 3 x 3 matrix, i.e. 3 rows (front, middle and last) with 3 seats in each row. The following information is known:
Chad sits immediately beside Dolly
Dolly sits in a row immediately behind the row in which Abe is sitting
There is no one sitting on one side of Chad
None of Elisa or Gregory sits immediately beside Abe
Bob sits in the last row
Which of the following statements is/are necessary to uniquely determine the seating arrangement of the seven friends?
Select an option, then click Submit answer.
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Abe sits in the same column as Chad and Bob with no one to his right
Also, since there is no one sitting to the right of D, D must be on the extreme right of the middle row. Thus, we have the following arrangement:
However, the position of E and G are not fixed. – Insufficient
GeneralLet us name the people Abe, Bob, Chad, Dolly, Elisa, Frank, and Gregory as A, B, C, D, E, F, and G, respectively. We can see that there are 3 × 3 = 9 seats, but there are only 7 people. Thus, the only possible way of distributing the 7 people across the 3 rows is that 2 rows would have 2 members each and one row would have 3 members. However, the exact number of people in a particular row is not yet known and further analysis of the statements needs to be done.
1st statement: C and D sit beside each other … (i)
3rd statement: The row in which C and D are sitting, has exactly 2 people sitting in it (since there is no one sitting on the other side of C) … (ii)
2nd statement: Since D sits in the row just behind A's row, the row where D (and C) sits must be either the middle or the last row
5th statement: Since B sits in the last row and the row where C and D sits has only 2 people, C and D must be in the middle row … (iii) Thus, it also follows that A must be in the front row … (iv)
4th statement: We know that neither E nor G sits beside
Thus, there are 2 possible scenarios:
If A is in the middle of the front row, none of E or G can sit in the front row; thus, they would sit in the last row … (v) If A is at either end of the front row, only in that scenario can one of E or G also sits in the front row … (vi) Thus, we have:
Also, in the middle row, since C has D on one side and a vacant seat on the other, C must be in the middle position. Thus, we finally have:
This is all that can be deduced from the main stem.
To answer the questions, we need to use the additional information contained in each question. -
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There is no person sitting in front of Dolly
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There is no person sitting in front of Elisa
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Abe sits in the same column as Chad and Bob with no one to his right and Elisa has no person sitting in front of her
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Abe sits in the same column as Chad and Bob with no one to the right of Abe or Dolly






