Dorian and Abigail play a game of tic-tac-toe. Dorian plays with crosses (x) and Abigail plays with noughts (o). However, we do not know who amongst Dorian and Abigail started this game.
In the game shown below, six moves have already been made:
o | o |
---+---+---
o | x |
---+---+---
x | x |
Who will win the game?
Steve makes a valid point, but I think the puzzle is soluble with some minimal assumptions:
Players do not have to play the best move, but:
If a line is blocked, the other player will no longer try to complete it
If a line can be completed, the player will try to complete it
If a line can be completed, the other player will try to block it
Number the 6 completed boxes:
12
34
56
Then boxes 1,3,4,6 could not have been completed last, because in each case X could have completed a line on X's current or previous move.
So the last box completed was 2 or 5.
If 2 was completed last, then X's previous move could have completed a line, leading to a contradiction.
If 5 was completed last, then O could not have played 2 or 3, because in either case, O could have completed a line.
So O played 1.
On the previous move, X played either 3 or 5. Arguably this breaches the rule against playing into a blocked line, but in either case X still has the chance of other unblocked lines as well.
So one possible way the game could have gone is:
5O, 3O,
1O, 2X,
6X, 4X,
Hence, O (Abigail) will win by completing the top row on her next turn.
Edited on June 29, 2022, 12:45 am
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Posted by broll
on 2022-06-29 00:42:29 |
No Subject
