1.

Somehow Mario gets out of the tunnel and then finds himself face-to-face with the evil gorilla Donkey Kong. Looking down, he saw that he was standing on a gigantic chess- board. He could see various chessmen standing along the board. Donkey Kong shouted, “Domination, total domination! Three challenges, and I want domination in them all!” Hint : In chess, domination problems mean arranging a minimum number of a specific type of chess piece such that all places on the board are attacked by atleast one peice. Total Domination: This is the same as domination but the spaces occupied by the attacking pieces should also be attacked by some other piece.How many ways can you arrange 4 queens such that they will dominate a 5*9 chess board?

Answer»

4
2
6
None of these

Solution :Arrange a queen in 4 of the 5 rows AVAILABLE preferably ADJACENT ones. So this leaves us with the last ROW unoccupied by queen. We have now successfully dominated 4 out of the 5 rows. Now, the positions of the queens determine the domination of the last row. Also, the row left unoccupied by queens can be changed to any of the REMAINING 4 rows which increase the number of solutions. On successfully trying out the different cases out, the number of cases of arrangement of queens to dominate the board turn out to be more than6.


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