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I was initially unsure whether “opposite corner” meant straight across or diagonally, but based on the later position information, it appears the q's intends diagonally opposite corners.

Since Abe moved first to B2, we can infer he started at A1. That makes E5 the diagonally opposite corner - Bea’s starting square and Abe’s destination square.
  • Early Game: Abe’s shortest winning path goes through C3 and D4. Bea should block this route: piece to D4
  • Later game: Abe is E4 and E5 away from his win. Bea must slow Abe’s progress while maintaining spacing: piece to D5 (D4 is occupied by Abe's piece).

ABCDE
1_
2a
3a
4b
5_
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Best way to solve these questions is to take help from the options instead of thinking all the possibilities.
First question is fairly simple and can be solved easily if we visualize that both the players should be sitting diagonally opposite to each other at the top left and bottom right corners
This would mean to block at least one of the space, player can only move diagonally


Second question can make you scratch your head if you start calculating all the scenarios, here it is best to take help from the options. Make a mark on the board for the given options and carefully observe how player A is actually only 2 moves away from winning unless stopped by B. Thus, logically B should block A in this move which eliminates the options - 3B, 3C and 5C.
Now the remaining options are - 4D and 5D. Given that we can't put moves in the adjacent blocks, 4D is also eliminated as invalid move.

Therefore, 5D is the only solution that's fitting.
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