Can You Count to Four? (4x4x4)
(Published on 6. October 2024, 13:00 by Tobias Brixner)
Background: I wanted to create “appetizers” to three of my 9x9 puzzles that I like particularly. Rather than just providing simple examples, the goal was for them to showcase aspects of the same logic and provide related solving experiences as the full puzzles. There is a thematic connection, as some quantity must be counted (up to four) in each part. Also, there is no given box or region division. I hope the result is challenging even though only realized on 4x4 grids. If you cannot find the time to do them all at once, there are also individual versions available, while the fourth one can only be solved after the first three.
If you like what you see, please check out the full versions of the puzzles. Some have a slightly different title which I adapted here to create a consistent set. Your comments are highly appreciated. Have fun!
Links: The solution code refers to the complete puzzle “Can You Count to Four? (4x4x4)”.
Only puzzle 1 “Can You Count the Whispers?”: 4x4, 9x9
Only puzzle 2 “Can You Count the Regions?”: 4x4, 9x9
Only puzzle 3 “Can You Count the Borders?”: 4x4, 9x9
Only puzzle 4 “Can You Count the Renbans?”: 4x4
Rules: The grid is divided into four 4x4 puzzles as marked by the thick black lines, each with separate rules listed below. Puzzles 1 to 3 can be solved independently.
Puzzle 1 (top left quadrant): “Can You Count the Whispers? (4x4)”
Place the digits 1-4 once each into each row and column. (There is no additional condition on regions.) Draw a single, non-intersecting loop that connects orthogonally or diagonally adjacent cells within puzzle 1 and acts as a Whispers line, i.e., adjacent cells along the loop differ by 2 or more. A digit in an arrow cell counts the not necessarily contiguous loop cells seen along the arrow direction outside of the arrow cell. For cells with more than one arrow, each arrow separately leads to the indicated number. Not all arrows are necessarily given.
Puzzle 2 (top right quadrant): “Can You Count the Regions? (4x4)”
Place the digits 1-4 once each into each row, column, and region of orthogonally connected cells. Regions must be determined. A digit in a cage counts how many different regions there are in all orthogonally or diagonally adjacent cells, including the caged cell itself, within puzzle 2.
Puzzle 3 (bottom left quadrant): “Can You Count the Borders? (4x4)”
Place the digits 1-4 once each into each row, column, and region of orthogonally connected cells. Regions must be determined. A cage contains the sum over the number of borders between regions as seen from that cell along all four orthogonal directions out to the edge of puzzle 3. A digit in a circle counts the number of borders between regions as seen from that cell along one of the four orthogonal directions out to the edge of puzzle 3. Only borders between regions are counted and not the outer edge of puzzle 3. Digits must not repeat in cages within puzzle 3.
Puzzle 4 (bottom right quadrant): “Can You Count the Renbans? (4x4)”
Place the digits 1-4 once each into each row, column, and region of orthogonally connected cells. Cells in puzzle 4 are grouped into the same regions with respect to each other as the corresponding cells in puzzle 3. Corresponding cells have the same relative position within their respective puzzles. When two cells in puzzle 1 are adjacent along the loop line and the corresponding cells in puzzle 2 are in different regions, the corresponding cells in puzzle 4 are connected by a segment of a Renban line. Every Renban line contains a set of consecutive digits in any order, without repeats. The cage counts the number of separate Renban lines.
Solution code: All digits of row 8 (from left to right) followed by column 6 (from top to bottom) without spaces.
