Epic Journey
(Eingestellt am 6. Mai 2026, 02:16 Uhr von Andrewsarchus)
About:
- This was my entry for turn 2 of season 2 of The Skunkworks League, hosted by damasosos92.
The prompt called for a pair of puzzles with different sized/shaped grids, with deductions in each puzzle affecting the other. Exactly one puzzle was required to have numbers in the solved grid, while the other puzzle was forbidden to have any numbers at all (not even within the clues).
General Concept:
- The concept I came up with for my entry involved cloning a loop from a large grid into a smaller toroidal grid. Within the larger grid, the loop does not intersect itself, but in the smaller grid, it is forced to cross itself due to the smaller space and toroidal geometry. Cells containing a crossing in the small grid map to two different cells in the large grid (one for the horizontal segment and one for the vertical segment).
Example:
Rules:
- 20x20 Grid:
In the 20x20 grid draw a single loop through the center of some cells.
The loop travels orthogonally, and does not cross itself.
The loop must visit every mountain symbol, and both water symbols.
The loop must not visit cells containing trees.
The loop also must not visit cells with stars in the center, but may visit cells which have stars on one of their vertices.
White stars are inside of the loop, and black stars are outside of the loop. - 10x10 toroidal grid (latin square):
Place the digits 0-9 once each in each row and column.
Clone the loop from the 20x20 grid into the 10x10 grid (without rotation or reflection).
The cloned loop will visit every cell of the 10x10 grid, and will cross itself.
At the crossings, each segment goes straight through the intersection.
Other than at these crossings, the loop does not overlap or touch itself.
The loop will never cross itself in a cell which contains a circle or a diamond (see below). - Circles (10x10 grid):
A number in a circle indicates the number of loop cells seen by the circled cell, including itself, in the row and column combined where vision is blocked by cell edges which are not crossed by the loop.
As the grid is toroidal, the vision is not blocked by the edge of the grid, unless that cell edge is not crossed by the loop.
Excluding cells which contain loop crossings, all possible circles are given. - Diamonds (10x10 grid):
A number in a diamond indicates the number of steps along the loop to a loop crossing, not necessarily the first, and without regard to a particular direction.
The referenced crossing will, however, be reached without crossing the toroidal grid boundary.
Excluding cells which contain loop crossings, all possible diamonds are given. - Loop Sections (10x10 grid):
The toroidal grid boundary divides the loop into eight sections.
Along four of these sections, the loop forms a mod-3 line.
Each sequential run of 3 cells along these sections must contain one digit from each of the three sets {0,3,6,9}, {1,4,7}, {2,5,8}.
Along two of the eight sections, the loop forms an entropic line.
Each sequential run of 3 cells along these sections must contain one digit from each of the three sets {0,1,2}, {3,4,5,6}, {7,8,9}.
The remaining two sections are unconstrained.
Every time the loop crosses the toroidal grid boundary, its nature changes, forming the periodic sequence:
mod-3, entropic, mod-3, unconstrained, mod-3, entropic, mod-3, unconstrained - Interactions:
A mountain symbol in the 20x20 grid corresponds to an intersection in the 10x10 grid.
The loop segment which passes through the mountain symbol is the clone of the segment in the intersection which matches its orientation (horizontal/vertical).
All possible mountain symbols are given.
A water symbol in the 20x20 grid corresponds to a circle clue in the 10x10 grid.
The loop segment which passes through the water symbol is a the clone of the segment in the 10x10 grid which passes through the corresponding circle.
Not all possible water symbols are given.
Neither of the two circles which correspond to the water symbols lie on one of the unconstrained sections of the loop.
Solution Check:
- Draw loops in both grids using green lines.
- In the 10x10 grid, show lines extending through the grid boundary for segments which wrap toroidally.
- Include the digits in 10x10 grid.
Play Online:
penpa+: Epic Journey
Lösungscode: Digits in the main diagonal (r1c1 to r10c10) of the 10x10 grid
Zuletzt geändert am 6. Mai 2026, 02:39 Uhr
Gelöst von Agent, mnasti2, mellowrobinson, aqjhs, lmdemasi, Rickium, nuzzopa, Kongfusion, mathics, damasosos92
Kommentare
Heute, 04:20 Uhr von damasosos92
Well, it surely is an epic journey. 5 entire hours to solve it.
am 6. Mai 2026, 02:25 Uhr von Agent
Completely insane!
