Babuschka

 Babuschka is a 1982 board game by Al Newman, published by Ravensburger.

 

BGG description:

Uses an 8x8 board with the 12 corner squares taken out. The pieces are nesting Russian dolls (8 each of small, medium and large, for 24 pieces per player). Reminiscent of Halma, the pieces attempt to cross the board and re-form on the opposite side. You only move the topmost of any Russian doll stack and you must land on an empty space or on top of a smaller piece. Checkers-like jumping is also possible. The clever part is that pieces underneath others are out of reach, thus you immobilize enemy pieces by covering them ... until you move away.

 

Rules also at BGG.

The game has an interesting and original property: it has perfect information, but requires the use of memory, since some pieces will become hidden during the match. Usually games of hidden information work on the opposite direction, less and less information stays hidden as the match advances.