A 1-person game/ puzzle (with a score), which involves a little math.

First, start with a n-by-n grid drawn on paper.

I suggest a grid of at least n=5, and (for serious fun) perhaps an n

of at least 10.

So, you start by writing 1 in any of the grid's n^2 squares.

You then write the 2 adjacent to the 1, the 3 adjacent to the 2, the 4

adjacent to the 3, etc, in a chain of increasing integers, in such

away that (ideally...) all n^2 integers are placed into the grid, one

integer (and ONLY one integer) per square.

(By "adjacent", I mean immediately next to in the direction of up,

down, left, or right, but *not* diagonally.)

And, oh by the way, the integers are to be placed so that EVERY pair

of adjacent squares contains two integers which are COPRIME with each

other...

(Again, "adjacent" is as defined above.)

So, you place the integers into the grid as far as you can until your

path cannot be continued for whatever reason.

And your score is the last integer you were able to write into a

square.

Here are my best, as of now, n=6 game, for examples:

21 22 25 26 27 *

20 23 24 * 28 29

19 18 1 2 3 *

* 17 6 5 4 *

15 16 7 8 9 *

14 13 12 11 10 *

(My score = 29)

And better,

1 2 3 34 27 26

6 5 4 33 28 25

7 8 9 32 29 24

12 11 10 31 30 23

13 14 17 18 * 22

* 15 16 19 20 21

(My score: 34)

(And I apologize if I missed that any 2 adjacent integers in my

examples have a GCD which is greater than 1.)

(And, double-check every time you write down an integer so as to make

sure that it is coprime with each of its neighbors, I suggest!

{unless playing on a computer, which should be checking for

coprimality for you})

Thanks,

Leroy Quet

## Thursday, September 18, 2008

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