Move By 3, by 2 (or by 1, by 2)
- From: "Leroy Quet" <qqquet@xxxxxxxxxxxxxx>
- Date: 17 Feb 2006 10:01:21 -0800
Start with a 6-by-6 grid.
Put a 1 in the upper-left square.
On each move you move either up, down, left, or right.
And you move alternatingly by 3 positions, then by 2,
then by 3, then by 2, etc.
At each move you write in the square you land in a
number which is one higher than in the square you were
previously at.
So, the distance between each 2m and 2m+1 is 2 squares
(skip over one square).
And the distance between each 2m-1 and 2m is 3 squares
(skip over 2 squares).
And you can only land on a square that doesn't already have
a number written in it.
And you cannot move off the grid.
Is it possible to fill each square with an integer (1 through 36)?
By hand I have only gotten 34 squares filled.
And I have not tried this for other sized squares.
Which n are such that it is possible to fill all n^2 squares
of an n-by-n grid?
And what if we instead move 1, then 2, then 1, then 2,...
Which n's are such that an n-by-n grid can be completely filled?
thanks,
Leroy Quet
.
- Prev by Date: Re: Origin and Explanation of the Laplace Transform
- Next by Date: Re: The Euler Equation - how was it arrived at?
- Previous by thread: Sign(S dot V ) knowing only the signs of S's components?
- Next by thread: The Euler Equation: What does "e" have to do with sine & cosine?
- Index(es):
Relevant Pages
|
