A friend of mine said he played a game with a friend that is played on a 4x4 grid. Two opponents have playing pieces that vary in color and height. The object is to get four like objects in a row - like tic tac toe. But! You must always make a move on your turn, and your opponent’s pieces (once placed on the board) can work in your favor.
Does anyone know what game this might be?
This sounds like Score Four, which is really a great strategy game for kids. A plastic pole was placed in the middle of each cell of a 4x4 grid; you could fit four beads of the game on each pole. Each player, one playing white and the other playing black, placed beads on the poles. You had to get, IIRC, four different groups of four beads in a row, either in a vertical row (all on the same pole), horizontally, or diagonally (one bead on the first level of a pole, one on the second, one on the third, and one on the fourth).
I loved it – it’s still at my parents’ house, and I may grab it next time I’m home so I can play it with my nieces and nephews. I will totally school them.
It sounds like Quarto.
Yes, it sounds much more like Quarto. Never heard of it but it sounds fun, too.