bonanova Posted March 19, 2009 Report Share Posted March 19, 2009 Imagine a 4x4 chess board with a lonely knight in the lower left corner. He decides to take a walk over to the lower right corner. A hop, actually; knights move in those silly L-shaped patterns. Being adventuresome, as knights are wont to be, he decides to visit as many squares as possible on his way, but without visiting any square twice. How many squares might he then visit, including his starting and ending squares? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 19, 2009 Report Share Posted March 19, 2009 (edited) Imagine a 4x4 chess board with a lonely knight in the lower left corner. He decides to take a walk over to the lower right corner. A hop, actually; knights move in those silly L-shaped patterns. Being adventuresome, as knights are wont to be, he decides to visit as many squares as possible on his way, but without visiting any square twice. How many squares might he then visit, including his starting and ending squares? Looks like 12 squares to me, working on the map now though. Edited March 19, 2009 by IDoNotExist Quote Link to comment Share on other sites More sharing options...
0 Pickett Posted March 19, 2009 Report Share Posted March 19, 2009 14 so far... +---+---+---+---+ | | 11| 6 | 3 | +---+---+---+---+ | 5 | 2 | 9 | 12| +---+---+---+---+ | 10| 13| 4 | 7 | +---+---+---+---+ | 1 | 8 | | 14| +---+---+---+---+ Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 19, 2009 Report Share Posted March 19, 2009 14 so far... +---+---+---+---+ | | 11| 6 | 3 | +---+---+---+---+ | 5 | 2 | 9 | 12| +---+---+---+---+ | 10| 13| 4 | 7 | +---+---+---+---+ | 1 | 8 | | 14| +---+---+---+---+ Well, he beat me to the map and his had more stops anyway. Good job Pickett! Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted March 19, 2009 Report Share Posted March 19, 2009 14 is the best I can do. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 19, 2009 Report Share Posted March 19, 2009 +---+---+---+---+ | | 11 | 4 |15 | +---+---+---+---+ | 3 |14 | 7 |10 | +---+---+---+---+ |12 | 9 | 2 | 5 | +---+---+---+---+ | 1 | 6 | 13 | 8 | +---+---+---+---+ Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted March 19, 2009 Report Share Posted March 19, 2009 +---+---+---+---+ | | 11 | 4 |15 | +---+---+---+---+ | 3 |14 | 7 |10 | +---+---+---+---+ |12 | 9 | 2 | 5 | +---+---+---+---+ | 1 | 6 | 13 | 8 | +---+---+---+---+ You must end in the lower right corner. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 19, 2009 Report Share Posted March 19, 2009 Oops , was tying this out on a chess board and came to 49 positions so far. Then I re-read the puzzle, and realized it was a 4x4 board . I'll have to try again. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 19, 2009 Report Share Posted March 19, 2009 (edited) Edit: Caught my own error, just a bit too late. Edited March 19, 2009 by hookemhorns Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 19, 2009 Report Share Posted March 19, 2009 14 is my top so far. Looking at the spoiler above, I did it a little differently, but it's still the best I've found. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 19, 2009 Report Share Posted March 19, 2009 16 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 19, 2009 Report Share Posted March 19, 2009 16 How? Show your grid please... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 19, 2009 Report Share Posted March 19, 2009 The most I have is also 14. Quote Link to comment Share on other sites More sharing options...
0 CaptainEd Posted March 19, 2009 Report Share Posted March 19, 2009 (edited) How? Show your grid please...Put 1 in lower left corner, 16 in lower right, A in upper right, B in upper left. There are only 2 squares you can reach to/from A, which means one is for entering and one for exiting. But they are the same as the two squares reachable from 1. So...when you leave 1, you must bounce over to A. Looks like this: B . . A(3) . 2 . . . . 4 . 1 . . 16 Similarly, you reach B just before bouncing over to 16, so it looks like this: 14 . . 3 . 2 15 . . 13 4 . 1 . . 16 Rotations don't matter, regardless of whether you jump right or left first, 4 and 13 are adjacent in the middle. Now, from 4, your moves are forced, and you only get 4 of them before you have to jump to 13. 14 5 . 3 . 2 15 8 6 13 4 . 1 . 7 16 So 4 squares are left over, the max path touching all four corners ending in lower right is 12. And you can't do 15 because you would end on the same color as you started on. Edited March 19, 2009 by CaptainEd Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 19, 2009 Report Share Posted March 19, 2009 14 is my top so far. Looking at the spoiler above, I did it a little differently, but it's still the best I've found. 15 is the best I can do. If you start in the lower left corner, it's the same as ending there. | 8| 5|12| 1| |13| 2| 9| 6| | 4| 7|14|11| |15|10| 3| | Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 19, 2009 Report Share Posted March 19, 2009 15 is the best I can do. If you start in the lower left corner, it's the same as ending there. | 8| 5|12| 1| |13| 2| 9| 6| | 4| 7|14|11| |15|10| 3| | The problem with this answer is you're supposed to go from lower left, to lower right.. not to upper right (by reversing your path). Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 20, 2009 Report Share Posted March 20, 2009 i could manage 14 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 20, 2009 Report Share Posted March 20, 2009 witout looking at the spoilers i can only do 12 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 20, 2009 Author Report Share Posted March 20, 2009 witout looking at the spoilers i can only do 12 Be sure to count the first and last square. Or we could just say how many squares were not visited. Quote Link to comment Share on other sites More sharing options...
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bonanova
Imagine a 4x4 chess board with a lonely knight in the lower left corner.
He decides to take a walk over to the lower right corner.
A hop, actually; knights move in those silly L-shaped patterns.
Being adventuresome, as knights are wont to be, he decides to visit as many
squares as possible on his way, but without visiting any square twice.
How many squares might he then visit, including his starting and ending squares?
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