releases soldiers from the hole in its underbelly. is a deadly combatant in its own right and will stay on the front lines to fight long after it finishes deploying its cargo.
individual puzzle tutorials provided upon request.
miscellaneous: @canon
Problem No. 024: Yajisan-Kin-Kon-Kan
Theme: Lying at the Center of the Galaxy
Picarats: 60
Rules: Mark some cells with diagonal double-sided mirrors such that no marked cells share an edge and all of the unmarked cells connect orthogonally in a single group. Each numbered arrow indicates the number of times its line of sight reaches a mirror, and each mirror redirects any line of sight that reaches it according to its orientation. Any cell with a numbered arrow can also be marked: such cells cease to indicate anything and can be true or false.
Problem No. 023: Ayeheya
Theme: yes, this is.
Picarats: 20
Play: https://puzz.link/p?ayeheya/6/6/4mnuu4007s02j
Rules: Darken some cells such that no darkened cells share an edge and all of the undarkened cells connect orthogonally in a single group. The position of darkened cells in each outlined region is point symmetric, and each orthogonal line of undarkened cells cannot cross more than one bold edge.
Problem No. 022: Pentominous
Theme: Willy-Nilly
Picarats: 60
Rules: Divide the grid into pentominoes such that no two of the same shape (including rotations/reflections) share an edge. Each lettered cell is part of a pentomino of the shape corresponding to its letter, as defined in the following image.
Problem No. 021: Statue Park
Theme: Treasure Map
Picarats: 35
Rules: Place the bank of shapes into the grid such that each shape segment occupies one cell, no shapes overlap or share an edge, and all of the unoccupied cells connect orthogonally in a single group. Shapes can be rotated/reflected. Black circles indicate cells occupied by a shape, and white circles indicate cells not occupied by a shape.
Problem No. 020: Tetro Stack
Theme: Eight Queens
Picarats: 40
Rules: Place one of each of the tetrominoes into the grid such that they do not share any cells or overlap a triangle. Each tetromino/triangle rests at the bottom of the grid or atop other objects such that it cannot fall straight down. Each tetromino cannot rest only atop triangles. Tetrominoes can be rotated/reflected.
Problem No. 019: Tetro Stack
Theme: U-Turn
Picarats: 20
Rules: Place one of each of the tetrominoes into the grid such that they do not share any cells or overlap a triangle. Each tetromino/triangle rests at the bottom of the grid or atop other objects such that it cannot fall straight down. Each tetromino cannot rest only atop triangles. Tetrominoes can be rotated/reflected.
Problem No. 018: Radar Pentominous
Theme: High Five
Picarats: 15
Rules: Divide the grid into pentominoes such that no two of the same shape (including rotations/reflections) share an edge. Each lettered cell is part of a pentomino of the shape corresponding to its letter, as defined in the following image. Each numbered cell is not part of a pentomino, and they each indicate the number of pentomino regions adjacents to it (including diagonally).
Problem No. 017: Statue Park
Theme: The Museum’s New Outdoor Exhibit
Picarats: 40
Rules: Place the bank of shapes into the grid such that each shape segment occupies one cell, no shapes overlap or share an edge, and all of the unoccupied cells connect orthogonally in a single group. Shapes can be rotated/reflected. Black circles indicate cells occupied by a shape, and white circles indicate cells not occupied by a shape.
The bank of shapes is based on the statues from the accompanying video, as demonstrated in the following image.
Problem No. 016: Sto-Stone
Theme: Name-Drop
Picarats: 30
Play: puzz.link
Rules: Darken some cells such that a single shape is present in each outlined region. These shapes are made up of darkened cells with shared edges, and they completely occupy exactly half of the grid if dropped straight down to the bottom and on top of one another. No darkened cells share a bold edge. Each number indicates the number of darkened cells in its region.
Problem No. 015: Isometric Statue Park
Theme: Many Ways to Unfold a Cube
Picarats: 60
Rules: Place the bank of shapes into the isometric grid such that each shape segment occupies one cell, no shapes overlap or share an edge, and all of the unoccupied cells connect orthogonally in a single group. Shapes can be rotated/reflected. Black circles indicate cells occupied by a shape, and white circles indicate cells not occupied by a shape.
in lieu of a puzzle this week, allow me to share an old puzzle level i made for super mario maker 2 that i’m still overall p pleased with.
Course ID: WQS-6KG-F0H
Problem No. 014: Easy as AC♭B♯
Theme: Enharmonic Equivalence
Picarats: 50
Rules: Label each empty cell with a letter in the indicated range, a flat symbol (♭), or a sharp symbol (♯), such that one of each character is present in each row and column. Each letter outside of the grid indicates the nearest letter visible along the cells in its line of sight into the grid. Additionally, each lettered cell nearest to an outside letter with a flat/sharp symbol shares at least one edge with a correspondingly symboled cell.
Problem No. 013: Arrow Skyscrapers
Theme: Waterfall (thanks for the shout-out!)
Picarats: 50
Rules: Label each cell with a number from 1 to 6 such that every number is present in each row and column. Each number in the grid indicates the height of a building at its cell, and each number outside of the grid indicates the number of buildings visible along the cells in its line of sight into the grid. Shorter buildings are not visible behind taller buildings. Each arrow crosses a path of cells: the sum of the numbers along the path is equal to the number at the circled cell.
Problem No. 012: Curve Data
Theme:
Picarats: 75
Play: puzz.link
Rules: Draw some figures in the grid such that all cells are occupied. These figures are made up of orthogonal line segments between the centers of cells, they do not share any cells, and exactly one glyphed cell is occupied by each figure. Each figure corresponds to its glyph such that it has the same orientation of segments interconnected in the same way, but the length of each segment of the figure can otherwise vary independently.
Problem No. 011: Curve Data
Theme: Here’s My Card
Picarats: 15
Play: puzz.link
Rules: Draw some figures in the grid such that all cells are occupied. These figures are made up of orthogonal line segments between the centers of cells, they do not share any cells, and exactly one glyphed cell is occupied by each figure. Each figure corresponds to its glyph such that it has the same orientation of segments interconnected in the same way, but the length of each segment of the figure can otherwise vary independently.
Problem No. 010: Futoshiki
Theme: A Puzzle, a Puzzle, and a Puzzle
Picarats: 10
Rules: Label each empty cell with a number from 1 to 4 such that every number is present in each row and column. Each inequality between cells indicates the size relation between its numbers.
Problem No. 009: Jigsaw Sudoku
Theme: Half-Trivial Double-Spiral
Picarats: 50
Rules: Label each empty cell with a number from 1 to 9 such that every number is present in each row, column, and outlined region.
Problem No. 008: XX Sudoku
dohz -Theme: Solve for X
Picarats: 65
Rules: Label each empty cell with a number from 1 to 9 such that every number is present in each row, column, outlined region, and diagonal. Additionally, a Roman numeral X is present on each edge shared by cells whose numbers add up to 10, and absent on each edge shared by cells whose numbers do not add up to 10.
upon the request of @hasenfu, i composed a tutorial on how to solve this puzzle (up to a point), which can be accessed under the cut.
every number must also be present in each of the two diagonals (the cells along which are colored gray for emphasis).
an x is present on each edge shared by cells whose numbers add up to 10, and absent otherwise.
importantly, that second stipulation clarifies that its inverse is also true. if an x is not present on an edge, then the cells that share that edge have numbers do not add up to 10. this is key.
let’s get started. this tutorial steps through at one placement at a time.
in the center region, the number 2 can be easily identified,
but afterward, we are immediately obliged to utilize the variant logic. sticking to the center region, the number 4 is somewhere in the right column, but where? examining the region’s bottom-right cell (r6c6), we note that a 6 is present at the cell just below (r7c6). an x is not present on the edge that these two cells share, so their numbers cannot add up to 10. since the number at r7c6 is a 6, the number at r6c6 cannot be a 4. refocusing on the center region, this means that the only available cell for 4 is r4c6.
for the rest of the center region, let’s actually examine r5c3 and r6c3. an x is present on the edge shared by these cells, which limits their numbers to some pair that adds up to 10: 1 and 9, 2 and 8, 3 and 7, or 4 and 6. already present on these cells’ shared column are the numbers 2 and 3, eliminating the pairs that involve them. in addition, the 6 at r5c4 not only prevents the number at r5c3 from being a 6, but also prevents it from being a 4, due to the lack of an x at these cells’ shared edge. this leaves 1 and 9 as the only pair that can be present at r5c3 and r6c3, but we still don’t know which number is at which cell.
what this does tell us is that, through the same logic we’d just used, the number at r6c4 cannot be 1 or 9. there is only one number remaining that it can be: 8.
this is all we can deduce within the center region for now, so let’s move on. in the bottom row, classic sudoku rules tells us that 2 can be at r9c1, r9c2, or r9c8. but remember that every number is present in each of the two diagonals as well. 2 is already present in both diagonals at r5c5, leaving r9c2 as the only available cell for 2 in the bottom row.
in the bottom-left region, our logic so far limits 8 to r8c1 and r8c3. however, an 8 at r8c1 would necessitate a 2 at r7c1, which is already present in this region. so 8 is at r8c3.
here’s where it gets complex.
this next step is what i consider to be the main catch of this puzzle. it’s where the most relevant break-in happens, after which the rest of the puzzle is a relatively smooth affair. here, it challenges us to keep a lot of observations in our heads at once. it’s mainly concerned with where the 4 is in the top-left-to-bottom-right diagonal, in tandem with where the 4 is in the third column. let’s break it down.
in the aforementioned diagonal, the 4 can only be either somewhere in the top-left region or at r9c9. but also observe where 6 and 8 can be in this diagonal. since both of them can only be at either r1c1 or r2c2, those cells are unavailable to 4, leaving r3c3 and r9c9.
turning our attention to the third column, 4 can only be present at either r3c3 or r9c3. and here’s the critical deduction: from the diagonal we’d just examined, we know a 4 is present at either r3c3 or r9c9. both cells share a row or column with r9c3, eliminating the possibility of a 4 being present there. this leaves r3c3 as the only available cell for 4 in this column.
and so the most difficult part is behind us. at this point, i trust that we’ve covered all of the logical techniques necessary for you to complete the rest of the puzzle on your own. the tutorial ends here, but if anyone who has read this is still stuck, let me know if you seek further guiding light. i’ll burn for as long as you need me to.
Problem No. 008: XX Sudoku
Theme: Solve for X
Picarats: 65
Rules: Label each empty cell with a number from 1 to 9 such that every number is present in each row, column, outlined region, and diagonal. Additionally, a Roman numeral X is present on each edge shared by cells whose numbers add up to 10, and absent on each edge shared by cells whose numbers do not add up to 10.
Problem No. 007: Surplus Yajilin
Theme: Nothing in This Hollow Heart
Picarats: 10
Rules: Darken some white cells such that no darkened cells share an edge and the undarkened white cells altogether form two loops. These loops only travel orthogonally between the centers of cells, they do not share any cells, and they do not cross/retrace themselves. Each numbered arrow indicates the number of darkened cells present along the line of cells in its direction up to the edge of the grid.
Problem No. 006: Yajilin
Theme: Nothing in This Solid Heart
Picarats: 10
Play: puzz.link
Rules: Darken some white cells such that no darkened cells share an edge and the undarkened white cells altogether form a loop. This loop only travels orthogonally between the centers of cells, and it cannot cross/retrace itself. Each numbered arrow indicates the number of darkened cells present along the line of cells in its direction up to the edge of the grid.
Problem No. 005: Battleships Yajilin
Theme: Self-Reference
Picarats: 25
Rules: Place the fleet of ships into the grid such that each ship segment occupies one white cell, no ships are adjacent (even diagonally), and the unoccupied white cells altogether form a loop. This loop only travels orthogonally between the centers of cells, and it cannot cross/retrace itself. Ships can be rotated, but they cannot be reflected. Each numbered arrow indicates the number of ship segments present along the line of cells in its direction up to the edge of the grid.
Problem No. 004: Arrow Sudoku
Theme: Raining Diamonds Sideways
Picarats:
Rules: Label each empty cell with a number from 1 to 9 such that every number is present in each row, column, and outlined region. Each arrow crosses a path of cells: the sum of the numbers along the path is equal to the number at the circled cell.
Problem No. 003: Computation
Theme: Critically Unprotected
Picarats: 15
Rules: Code a computer program that solves the question in bold in under one minute. Optionally, solve it through some other method instead.