As I explained recently, the Hidoku puzzle (Hidoku's Rules) is very versatile, the grid could take many shapes, like square Hidoku # 1 or even drawing forms likes Hidoku # 2. But another aspect that can be modified is the shape of the cells. In the last described puzzles all the cells are square. But nothing prevent us to modify this, by example we could have hexagonal cells (six sides). When the shape of the cells are modified then this could impact how go from on cell to another one to find the path. By example with a conventional square grid with square cells (showed in the next figure). It is agreed that a move from a cell can go horizontaly, verticaly or diagonaly of only one step.
So from the blue cell we can reach the 8 red cells.
But we can generalize that we could move from one cell (the starting cell) to any other cells that touch one corner of the starting cell. And we can apply this rule to any shape of cell (instead of saying to move horizontaly, verticaly, etc). Like for the octogonal cell. The following figure illustrates a portion of a grid with hexagonal cells. From the blue cell, with this rule (going to cell that touch a corner of the starting cell),
we are able to reach any of the six red cells. Notice that with hexagonal cells we are able to reach at most 6 cells instead of 8 for the square cells. All this is related to the specic geometry of the cells. A corner of a square is able to touch three cells and a corner of an hexagonal cell is able to touch two cells only.
Then just to tease you I present you three Hexagonal Hidoku puzzles. Try to find the path strating from the cell 1 and finishing with other cell having a circle.
1)
The printable files PDF
Puzzle: hido_1_6x6_16_00004.pdf
Solution: hixa_1_6x6_16_00004_sol.pdf
2)
The printable files PDF
Puzzle: hixa_1_6x6_14_00005.pdf
Solution: hixa_1_6x6_14_00005_sol.pdf
3)
The printable files PDF
Puzzle: hixa_1_7x7_20_00009.pdf
Solution: hxa_1_7x7_00009_sol.pdf
Enjoy !
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