Knight Knight Sleep Tight II
Can a chess knight traverse every square of this letter (for K night), landing on each square exactly once?
It does not have to be a closed tour (i.e. the end doesn't need to meet up with the beginning).
This problem is part of the Knight Knight Sleep Tight set.
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1 solution
Label the grid with the lower left square being (1,1). Assume that we are at square (4,6) and have somehow landed exactly once on every square of the figure except for squares (5,8) and (6,7). Now our only possible moves are from (4,6) to (5,8) or (6,7). Lets say we move to (5,8). Now, we only need to land on (6,7), but there's a problem: At our current position (5,8), we cannot get to (6,7) unless we land on (4,6) again. So we have landed 2 times on square (4,6) and the answer is NO! . We would have concluded the same if we had first moved from (4,6) to (6,7). Also, the assumption we made at first is wrong since squares (4.3), (5,1), and (6,2) also cannot be all covered without going through square (4,3) twice.
Again, nice problem Stephen Mellor! KEEP IT COMING!!!