On the 8×8 chessboard there are two identical markers in the squares a1 and c3. Alice and Bob in turn make the following moves (the first move is Alice’s): a player picks any marker and moves it horizontally to the right or vertically upwards through any number of squares. The aim of each player is to get tothe square h8. Which player has a winning strategy no matter what does his opponent? (There may be only one marker on a square,the markers may not go through each other.) The 8x8 chessboard consists of columns lettered a to h from left to right and rows numbered 1-8 from bottom to top
Problem
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Tags: ToT
itslumi
25.06.2020 19:16
Write with $P$ winning positions for the player that find the Marker in that place and now is his turn to play,and with $N$ the losing positions for the player that find the Marker in that place and now is his turn to play. We find out that all the cordinates in diagonal from $(a,1)$ ,$(b,2)$,...,$(g,7)$ are losing positions $N$,thus $A$ needs to start the game in a loosing position which implies that $B$ has a winning strategy. P.s.Does anyone has the official solutions
ZeroTolerance
25.06.2020 19:37
I believe above solution works only when there is only one marker, we can not guarantee that second player always can reach diagonal squares
itslumi
25.06.2020 19:40
ZeroTolerance wrote: I believe above solution works only when there is only one marker. I dont belive so,both Markers are in $N$ positions btw if you have any other solution,please post it
itslumi
25.06.2020 21:36
ZeroTolerance wrote: I believe above solution works only when there is only one marker, we can not guarantee that second player always can reach diagonal squares why he need so,in diagonal squares are the loosing positions