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If you like chess and/or Math and/or puzzles, here is a brain-teaser for you:
Let's consider two games: a) there is a rook on a1 b) a king on a1. Two players turn by turn can move the piece towards h8 (moving either right, up, or, in the case of a king, digonally up-right). The player to place the piece on h8 wins. Who of the players has the winning strategy in each case, and how should he act?
1. Written by
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on 11:22 12 2011 .
a) The player who moves second should move the rook the back to the a1-h8 diagonal after the first player has made his move, to win.
b) The player who mover first should move the king to b2, then he should mirror the second players move to win. (e.g. after c2 play d2, after b3 play b4, and after c3 play d4).
2. Written by
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on 11:54 12 2011 .
ted d.
must be some additional rules, restrictions, or criteria - question doesn't have sufficient info to solve.
3. Written by Alexandre on 12:25 12 2011 .
ted d.
In the caso of Rook, anyone who reaches the squares from h1 to h7 or the squares from a8 to g8 loses, as the next player will reach h8 on his move. So, anyone who reaches g7 wins, which means that you can win by thinking in a smaller board, free of file h and the rank 8. Repeat the process until you find the correct move.
4. Written by
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on 01:20 14 2011 .
alexander
Let's say the players are named Alice and Bob and Alice will move first.
a) Since the rook can only move up and right, all paths from a1 to b8 will have the same length (for each move right eventually there will be a move up). The number of moves will alwazs be exactly 14 (7 right + 7 up), so Bob will always win no matter of the strategy.
b) The most direct path is the diagonal a1-h8 which has length 7, i.e. Alice will win if she could enforce the mofe sequence to either follow the diagonal or 'deviate' an even number of steps. Alice begins with 1.b2 and proceeds with the next diagonal square as long as Bob also plays the diagonal along (e.g. 1...c3 2. d4). If Bob moves up or right from the diagonal square, he will land on a white square and will exand the shortest path by one move taking the advantage. In this case, Alice should compensate by making a move in the same direction (e.g. 1. b2 b3 2. b4 or 1. b2 c2 2. d4). Similarly, a diagonal move by Bob should be followed by a diagonal move by Alice (basically the strategy by Pim Verkerk is spot on - first move should be b2 and then Alice should mirror Bob's moves).
5. Written by
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on 01:45 17 2011 .
6. Written by
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on 22:34 19 2011 .
alexander
After reading the solutions offerred by Alexander and Alexandre, I now understand what the problem was in the first place. I must have had problem with slightly awkward english.
The solutions/strategies, of course, are correct. 2nd player wins for Rook; 1st player wins for King.
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