Designer Diary: Tangram City

by Korea Boardgames

[Editor’s note: Uwe Rosenberg doesn’t use BGG much, but he does write about his creations, so publisher Korea Boardgames is posting this diary on his behalf. —WEM]

Polyominoes are created by connecting squares together — not neatly from left to right, but crisscross as long as they touch edge to edge. With 3/4/5/6 squares, you can construct 2/5/12/35 polyominoes, and this sequence continues further: 108, 369, 1285… Somehow, mathematicians around the world want to stay busy.

I was surprised by how mathematical everything related to polyominoes is to read about. It involves rotations and reflections. When you invent games with polyominoes, you bring them to life. You notice which parts can be nicely puzzled together and which ones give you trouble…and you notice which parts are especially enjoyable to twist and turn. My favorite piece is the 2×3 rectangle in which the third column has shifted down by one position.

Through a series of games, I’ve gained a better sense of polyominoes. I kept the squares for the polyominoes and drilled round holes into various squares, which significantly increased the number of different pieces. The holes should trigger something when placed on specific squares. This resulted in the games Indian Summer and Spring Meadow. I’ve made the polyominoes more variable by allowing the dismantling of a partial square at certain ends. For pen-and-paper games, I’ve introduced polyominoes that are not directly connected to each other. Of course, something like this works only when you draw out the polyominoes. This led to the creation of the games Patchwork Doodle and Second Chance.

Even these insights would be worth mathematical classification. However, the mathematician (probably a man) would likely prefer to count how many polyominoes have a hole instead of a square…

Continuing in my exploration, I have also diagonally cut individual squares. This created entirely new pieces that resemble the famous Tangram puzzle in terms of shapes. As in Patchwork Doodle, your goal is to complete as large of a rectangular area as possible, round by round, without any gaps. (You can use small triangles (half squares) to fill in any inaccuracies.) Each player is provided with the same pieces, and the game evolves differently for each player due to varied starting formations. This game will soon be available as Tangram City, specifically at the Korea Boardgames booth (2-C148) at SPIEL ’23.

Thematically, we decided to turn this puzzle into a city-building game. The city’s mothers and fathers should design their city in a balanced way, distributing both sides of the tiles evenly on their landscape board – an additional challenge to keep players engaged even in the tenth game.

Meanwhile, I’ve also developed two games in which isosceles triangles are adjacent instead of being formed into squares. There isn’t a name for such formations – and mathematical considerations are completely absent, at least as far as I can find. Perhaps one of these games will appear someday, and perhaps it will serve as a basis for scientific examination by some mathematician. Counting holes works wonderfully here as well.

Naturally, there are also composite hexagonal tiles, but each hexagonal tile consists of six isosceles triangles – essentially, it’s just a special case of the “polytriangelinos” I’ve just described. I’ll take the liberty to call them that.

Yours sincerely,

Uwe Rosenberg