Ossetian Checkers derives from Ossetia. It is a region in the central Caucasus, the northern areas of which are in Russia, the southern areas, in the Republic of Georgia. Ossetians presently number some 600,000. (Funk & Wagnall's Enc.)
The object is to take the enemy checkers or block them so that they cannot move. Checkers step ortogonally forward or diagonally forward. Capture is done by the short leap in any direction, also to the sides and the backward directions. Continuous capture is allowed. A captured checker is immediately removed from the board. Capture is not mandatory. There is no promotion at the last rank. Pieces that end up here cannot move, but can still capture.
The standard game board is 7x7 and pieces moves on the intersections of a grid. The game is sometimes played on the larger 9x9 board, when each player has 27 pieces.
Apparently, variants exist when additional pieces are placed on intersections in the middle of the squares. In this case 33 and 43 pieces are used, respectively.
My source is referenced below. The game seems to work, although the 9x9 version is long-winded.
The above link gives this source:
Zapletal, Miloš. 'Velká kniha deskových her'. Mladá Fronta, Praha, 1991.
© M. Winther, 2010 February