Prasun Vs Azhaghu (Tic-Tac-duel - 3)
Once Prasun and Azhaghu were playing the famous game of Tic-Tac-Toe. Prasun plays the cross i.e '
X
' and Azhaghu plays a circle i.e '
O
'. In the above picture , now its Azhaghu's turn. However this time Azhaghu plays a wrong move, which causes him to eventually lose the game (so sad).
What are all the possible places that Azhaghu could put an ' O ' which will make him lose to Prasun? Enter your answer as the sum of all these squares.
Details and assumptions:
-
A player can put his symbol only once every move and a player cannot say pass his turn.
-
Assume that Azhaghu and Prasun both play perfectly after Azhaghu's wrong move.
For more , try this set .This problem is created by me!
The answer is 16.
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2 solutions
Moderator note:
Great visual aids!
Yes, basically, if he places 'O' in a place other than 1,4, I can easily create a fork that cannot be defended and easily win.
One can note that I can only make 2 types of fork here: one is the 7 shape along 2,1,4 and the other is the laterally inverted 7 shape along 3,4,1.
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Congrats , you won this round successfully!
And we call this as the V tactic !
Let's examine each move,
- First at 1 .
If this happens, Prasun will surely place his next move on 5 to defend himself. Now, Azhaghu can place his move on either 3 to defend himself. Now, Prasun will place his move on 2 or 4 to get the best chances of winning, assuming that he places it at 4 , Azhaghu will place his next move on 5 and the match ends in a draw. . . . . . . . ( i )
- Next at 2 .
If this happens, Prasun will surely place his next move on 4 to get the best chance of winning. Now, Azhaghu can place his move on either 3 or 1 , assuming that he places it at 1 , Prasun will place his next move on 3 and completes a row. . . . . . . . . ( i i )
- Now at 3 .
If this happens , Prasun will surely place his next move on 1 to get the best chance of winning. Now, Azhaghu can place his move on either 2 or 4 , assuming that he places it at 2 , Prasun will place his next move on 4 and completes a row. . . . . . . . . ( i i i )
- Now, at 4 .
This will lead to a similar case as in ( i i ) .
- Next at 5 .
This will lead to a similar case as in ( i i i )
- Finally at 6 .
If he does this the play will continue as it was in ( i ) .
Hence we conclude that Azhaghu can play his best by using the ( i ) tactic in his tic tac toe game.
So, Azhaghu could have lost if he had placed his move on 2 , 3 , 5 or 6 . So the answer is 2 + 3 + 5 + 6 = 1 6
If he play 2 or 3 then he is not playing 'perfectly'. He sure would lose. He can only play 5 or 6 to have the chance of winning.
I would say the answer is 21. Any mobe lead him to loose
We see that if Azhaghu does not place his symbol on corners , he loses. So the answer is 2 + 5 + 6 + 3 = 1 6