Broken Sign Blog
#145: "One Utopia" Pack
12 June 2024Let’s skip a few showcases and jump to the present. I made this pack of 16 small puzzles with a common variant as an unofficial entry for Logic Showcase 59, “There Can Be Only One”.
The prompt asked us to make puzzles in an existing genre with an extra rule of the form “there is exactly one [X]”. “X” may either be something that normally can’t appear in the solution, or something which can normally appear an arbitrary number of times.
After playing with a few ideas of the former variety (i.e. breaking a rule by adding some “thing” to the puzzle), I really wanted to make something in the latter category. It took a while to come up with something I liked, but eventually I hit upon this idea inspired by Jamie Hargrove’s genre Utopia: in a region division puzzle, there is exactly one gridpoint that is not used by any region boundaries.
But now I had a problem: what base genre do I pick? And so I just started making lots of small puzzles in every suitable genre I could think of. Even a few shading genres (interpreting the boundary between shaded and unshaded cells as a region border). And I’m really happy with how this set turned out. There’s a lot of variety in how the variant affects the different genres.
For the first time on this blog, I’ve also assigned difficulties to the puzzles. The scale will look a bit weird (it goes from 2 to 6), because I’ve tried to calibrate it roughly to the difficulty ratings used in the Toketa puzzle books, which use a scale of 1 to 5 with “5+” used for the occasional extra hard puzzle.
Rules: In each of these puzzles, exactly one internal grid vertex is not used by any region boundaries. In other words, there is exactly one 2x2 that does not contain any region boundaries. For genres that usually use shading, each shaded or unshaded group of cells is considered a region.
Rules: Divide the grid into rectangular regions of orthogonally connected cells. Each region must contain exactly one circle. A number in a circle represents how many cells are in the region the circle belongs to.
Rules: Shade some cells so that each orthogonally connected area of only shaded or only unshaded cells contains exactly one clue. Some clued cells are given as shaded, and unshaded clues may not be shaded. A clue represents the size of the area of shaded or unshaded cells that the clue belongs to.
Rules: Divide the grid into regions of orthogonally connected cells. Two regions of the same size may not share an edge. Clued cells must belong to a region containing the indicated number of cells.
Rules: Shade some cells so that all areas of orthogonally connected shaded cells are rectangular and all areas of orthogonally connected unshaded cells are not rectangular. A clue represents the size of its group of shaded/unshaded cells.
Rules: Divide the grid into regions of orthogonally connected cells. Each region must contain exactly two circles and have an area that lies between the two numbers in the circles, exclusive.
Rules: Divide the grid into regions of four orthogonally connected cells. Clued cells must have the indicated number of region borders or grid borders surrounding them.
Rules: Shade some dominoes of cells to divide the grid into unshaded areas. Shaded dominoes may not touch orthogonally. Clues cannot be shaded, and each orthogonally connected area of unshaded cells contains exactly one type of clue, and all instances of it.
Rules: Divide the grid into regions of four orthogonally connected cells so that no two regions of the same shape share an edge, counting rotations and reflections as the same. Clued cells must belong to a region with the tetromino shape associated with that letter.
Rules: Shade some cells so that the shaded cells are all connected orthogonally by other shaded cells to the edge of the grid, and the remaining unshaded cells form one orthogonally connected area. Clues cannot be shaded, and represent the total number of unshaded cells that can be seen in a straight line vertically or horizontally, including itself.
Rules: Shade some cells so that clues represent the total size of the orthogonally connected areas of shaded cells that share an edge with the clue. Clued cells cannot be shaded.
Rules: Divide the grid into regions along dotted lines. Each number indicates the total number of cells within its region that can be seen horizontally or vertically from that cell, including the numbered cell itself (line of sight is blocked by region boundaries). All numbers that are maximal within their region are given, and no other numbers are given.
Rules: Divide the grid into regions of edge-connected cells, such that each region’s outline has rotational symmetry. Two regions containing the same number of cells cannot share an edge. Clued cells must belong to a region containing the indicated number of cells.
Rules: Divide the grid into regions of orthogonally connected cells, each containing exactly one clue. The numbers in a clue indicate all of the different lengths of runs of consecutive cells within its region, vertically and horizontally. Lengths may be repeated, but each given length must be represented at least once.
Rules: Divide the grid into regions of orthogonally connected cells such that each region contains exactly one type of clue, and all instances of it. Every grid point (including on the edges) from which three or more region borders or grid borders extend is marked with a dot.
Rules: Divide the grid into regions of orthogonally connected cells, each containing exactly one compass. A number in a compass indicates how many cells belong to its region that are further in the indicated direction than the compass itself.
Rules: Divide the grid into regions of orthogonally connected cells. Each region must contain exactly one white and one black clue. Black clues indicate the total area of the largest rectangle fully contained within the region. White clues indicate the total area of the smallest rectangle containing the entire region.