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Background

Back in March, I posted this question on the Puzzling Stack Exchange asking how many clues were needed to create a 4x4 Hidato puzzle with a unique solution.

Sometime after this, I took a break from doing this until recently, when I decided to try to make a minimally clued 7x7 Hidato.

I have currently created the following 7x7 Hidato with 16 clues, and am currently working on figuring out whether this is the minimum or not.

Goal of Hidato

Fill the grid with consecutive numbers such that they connect orthogonally and diagonally.

Goal of this puzzle

Solve the following Hidato

The puzzle

+--+--+--+--+--+--+--+
|1 |  |30|26|  |  |  |
|  |  |  |  |  |20|  |
|  |35|  |  |  |  |19|
|37|  |  |  |  |  |  |
|  |39|13|  |  |  |49|
|40|  |  |  |  |  |  |
|  |42|43|46|10|  |7 |
+--+--+--+--+--+--+--+
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6
  • $\begingroup$ @BeastlyGerbil Sorry, to solve the puzzle $\endgroup$
    – CrSb0001
    Commented May 21 at 19:10
  • $\begingroup$ I believe the '10' clue can be left out, and it is still a valid hidato. Because 1-7 and 46-49 is forced, there is only one way for the 7 to leave the corner: there is no need for the 10 at that place. Leaves only 15 clues ;) $\endgroup$
    – Lezzup
    Commented May 21 at 21:48
  • $\begingroup$ @Lezzup Agreed, and you can also simultaneously remove 40, leaving 14 clues. $\endgroup$
    – RobPratt
    Commented May 21 at 22:59
  • 1
    $\begingroup$ I found a 8-clue 7x7 Hidato with unique solution. $\endgroup$
    – Bubbler
    Commented May 22 at 0:17
  • 2
    $\begingroup$ Now I've got one with 7 clues. The two puzzles can be found here. $\endgroup$
    – Bubbler
    Commented May 22 at 1:44

1 Answer 1

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5
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Solution:

enter image description here

Step by step:

1:

Firstly, the diagonal is forced

enter image description here

2:

Now, there is only one way for 46 to connect to 49. This forces the 11 to go left of the 10, and only one configuration for the 8 and 9.

enter image description here

3:

Working forwards and backwards at the same time, the chain from 46 to 37 is all forced, starting with the 45, and this leaves one space for 12

enter image description here

4:

Now the 13 has to go through the 3/4 gap to reach the 19. If it goes straight across to the 19, it will isolate the cells below, so has to loop round to these cells. In fact, the cell below the 19 has to be 18, as no other number is possible. Backtracking, this fills in the path.

enter image description here

5:

Now the 30s have to loop round the top left as nothing else can reach this spot

enter image description here

6:

Finally, the 20s have to loop around the top right, and the cell below the 20 must be connected to it, as the 26 cannot reach, and hence must be 21. And hence the solution is forced:

enter image description here

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