I just rememebered a game of sinking war ships we sometimes played when I was a kid, mainly against my mom, and it maybe increased problem solving skills later, but we did not play it so often.
Mostly there are just two players. Each player has a grid boxed ordinary writing or counting paper and a pen. They choose a square of a suitable size, for example 8 times 8 boxes, and a nice number of war ships fitting well to it, for example one row of five boxes, two ships of four, three ships of three boxes in a row, four ships of two and five ships of one box. They also number the boxes by marking numbers from 1 to 8 to the side and letters from A to H to the top so that each box is easy to refer to.
Then they each secretly, without showing to the opponent, draw the ship outlines to their water area. No twio ships may be side by side but corners touching is ok.
Then they try to guess where the ships of the other player are and hit them to sink the ship under the water. They each in turn mention a box, for example B3, and the other one checks if there is a ship there in her/his paper, and so she/he answers "It hit but did not yet sink." or "Flew past." if there is no ship there, or "It hit and it sank." if there was a ship and it's all places had been hit. So they need another box where to mark their guesses theyt have already made: just cross the box in quaéstion and make some mark of whether there was a ship there. Similarly you can on your own ships' pool make markings of the guesses the other onbe has made.
Somehow I feel that this is good for making guesses about possible solutions and for building upon the werll working ones.