#DILR-19




Three children, Rekha, Shankar and Mukesh, were playing the game of Tic-Tac-Toe, on a grid of 3 × 3 squares. Each game was played by all the three children, with the rules slightly modified from the usual, as described below.
  1. Each person has his/her own symbol, referred to as his/her 'mark' and in every turn, he/she places the same mark on the grid.
  2. The columns are labelled A to C, from left to right, and the rows are numbered 1 to 3, from top to bottom. The position of a mark on the grid is given by the combination of the column and row labels of the square in which it is placed. For example, a mark in position C2 means that the mark is in column C and row 2.
  3. The first person to play a game can place his mark on any square in the 3 × 3 grid except B2.
  4. In every subsequent turn, each person has to place his/her mark in any empty square, which is
  1. not in the same row or column as that of the mark that was placed immediately before his turn
  2. not in any diagonal position in any of the four possible directions to that of the mark that was placed immediately before his turn.
For example, if the first person places his/her mark in C2, the second person cannot place his/her mark in any square in column C or any square the 2nd row or in the squares in the diagonal positions to C2, i.e. B1 and B3.
  1. The first person to get three of his/her marks in a straight line (horizontally, vertically, or diagonally) in the grid is the winner.
  2. The game ends in a tie if all the nine squares are full or if it is not possible to place any other mark in the remaining squares, without having a winner.
A fresh grid is drawn at the beginning of each game.
The marks of the three persons, Rekha, Shankar and Mukesh, are 'X', 'O' and 'I' respectively. It is known that in any game that they played, the first person to play did not place his/her mark in B2.


If a total of 34 games were played, how many games ended in a tie?
Enter your answer as ‘-1’ if you think that the answer cannot be determined with the given information.



In one of the games, Rekha, who was the first person to play, ended up winning the game. Which of the following options could represent the grid immediately after she placed her first mark?

 a)
   
 b)
   
 c)
   
 d) Data Inconsistent 


If 'I', 'O' and 'X' were the first three marks to be placed on the grid in that order, then who among the following could not have won that game?

 a) Mukesh    
 b) Rekha    
 c) Shankar    
 d) None of the above    


If Mukesh, Shankar and Rekha played a game, taking turns in that order and Mukesh did not win the game, which of the following options could represent the grid immediately after Rekha placed her first mark?

 a)
   
 b)
   
 c)
   
 d) More than one of the above    








Solutions:-

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