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Cipra City Tiles, a map on a Donut

We’ve been captivated by the Cipra Loops tiles, and we’ve added another Barry Cipra invention to our lineup. Cipra has again found inspiration in the work of Sol Lewitt, who often explored the possible combinations of graphic idea. For these tiles, that idea is vertical, horizontal, and diagonal lines, and Cipra created a tile for each unique combination. The tiles are oriented, since rotation could violate the uniqueness of a tile. In the image below, the orientation is indicated by the blue triangle. All blue triangles will point in the same direction when composing the 16 tiles. Can you convince yourself that all possible combinations of roads are represented?

Barry Cipra’s oriented tiles with horizontals, verticals, and diagonals

The goal is to arrange the tiles in a 4×4 map, so that all lines run from edge to edge. We thought of the lines as roads, and created tiles that look like this:

Cherry Arbor’s interpretation of Cipra’s tiles

This is the kind of puzzle that starts out seeming easy, but can get difficult as you try to finish. Here is a potential start:

a possible part of a Cipra City map

This, on the other hand, is off to a bad start. Can you see why this cannot be part of a Cipra City map?

not part of a Cipra City map

Here’s one that’s a bit more subtle. Can the arrangement below be part of a map?

What about this arrangement?

Remarkably, if you find a solution, it will also work as a map on a torus (see Cipra Loops for more about the torus)! In that case, the roads do not end at the edge of the map. Instead, the road appears on the side opposite where it seems to exit, and continues in the same direction. So every road is actually a loop on the torus, and every loop passes through exactly 4 tiles.

Cipra City tiles are available in our store.