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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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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 by IDoNotExist
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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!

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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 by CaptainEd
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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| |

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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).

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