Wow, that was tricky.
 
x x x . . . .
. . x x x . .
. . . . x x x
. . . x x . x
. x x x . . .
 
The arrangement of the top three rows is the only way I 
could find to let the bottom two rows join.  Nice problem. ::)
- Matt Elder

Mr. Kurchan's pawn placement problem:
xxxoooo
ooxxxoo
ooooxxx
oxoxxoo
oxxxooo
Nice one, this.
JP Ikäheimonen

My solution (. is an empty square, * is a pawn)

. . . * * * .
. . * * . * .
* * * . . . .
. . * * * . .
. . . . * * *

Mike Shafer

For the 15 pawns in a connected shape in a 5x7 grid with no 4 in any line,
I found this solution:
PPP....
..PPP..
....PPP
.P.PP..
.PPP...
Joseph DeVincentis

Aha!
I have found it.
 
X
X          X  X
X  X          X
    X      X  X
    X  X  X
        X
        X
 
Take smallest dimension.  5 in this case.  Multiply by rule of three.
15.  Maximum number of pawns possible for that size grid.
Dick Saunders Jr.