On Jun 1, 5:09=A0pm, Ed Murphy <emurph...@[EMAIL PROTECTED]
> wrote:
> don.lo...@[EMAIL PROTECTED]
wrote:
> > A0 33 954. found body at intersection. min dist /upper bound/
> > detective must walk to grid search area.. =A0PUZZLES..
>
> > [crime victim could have staggered (? sp.) n blocks =3D x+y. ]
Thank you Ed M,
we assumed that the detective must traverse the complete line segments
within 'radius' of n blocks.
the victim staggered n blocks and (collapsed) at an intersection =3D=3D
the 'origin.'
he followed the path of the street.
i assume road and footpaths /side-walks/ is one line.
probably not sufficient to only visit the intersections.
must also walk line segments. what do you think?
>
> > area of square-diamond =3D 2n^2.
> > detective walks 2 new sides of perimeter squares [spiral] and double 3
> > axes.
>
> Attempted translation into English: =A0What is the minimum length
> of a path that visits all points (x,y) where x and y are integers
> and |x|+|y| <=3D n?
>
> Requests for clarification: =A0Must the path begin at (0,0)? =A0Can
> it cross points (p,q) where neither p nor q is an integer?
>
> Sample paths for n =3D 1:
>
> =A0 * (0,0) to (0,1) to (0,0) to (1,0) to (0,0) to (0,-1) to (0,0) to
> =A0 =A0 =A0 (-1,0) [length 7]
>
> =A0 * (0,1) to (0,0) to (1,0) to (0,0) to (0,-1) to (0,0) to (-1,0)
> =A0 =A0 =A0 [length 6]
>
> =A0 * (0,0) to (0,1) to (1,0) to (0,-1) to (-1,0) [length 1 + 4*sqrt(2)]
>
> =A0 * (0,1) to (1,0) to (0,0) to (-1,0) to (0,-1) [length 2 + 2*sqrt(2)]
>
> > what about spherical globe? igloo? ice-house.
>
> All points (x,y,z) where x and y and z are integers, |x|+|y|+|z| <=3D n,
> and (for an igloo) x >=3D 0.
donald s. mcdonald. 3-6-08. cheers,
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