11
$\begingroup$

Rule of Hidato:

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

Solve the following three Hidato puzzles.

8 clues

7 clues

6 clues

You can solve these on Penpa: 8 clues, 7 clues, 6 clues.

Improve this question
$\endgroup$

2 Answers 2

Reset to default
11
$\begingroup$

Is this a race to the bottom? I solved the 8- and 7-clue puzzles before you edited to make the 6-clue one. (Edit: I also added a solve path for the 6-clue)

8-clue solution

8-clue solution

7-clue solution

7-clue solution

6-clue solution

See mathlander's solution.

Solve path (8-clue)

Trivial deductions: 8-1

This is the only way to escape the bottom-right after 17-20: 8-2

Then the solution follows.

Solve path (7-clue)

Trivial deductions: 7-1

There is a risk of cutting off the top-right with the 1-7 path, so I speculated that there must be a two-way path to the top-right (I believed that the ending of 39-49 couldn't possibly finish in the top-right). So the only way is this: 7-2

The 19-25 forces the following. And continuing with the assumption of the two-way travel to the top right: 7-3

Then the solution follows.

Solve path (6-clue)

Trivial deductions 8-0

Notation: (i, j) = i-th row, j-th column.

Now (1, 2) can either be 49 or 8. It cannot be 8 because it forces the following and breaks 22-26. 6-0'

So it is 49 and gives the following: 6-1

13 cannot be in (5, 6) because it either cuts off 1-9 or isolates (5, 7), but the 49 is already placed. So 13 is in (5, 7), and we have: 6-2

To have 33-47, I must leave a two-way path in each of the top-right and bottom-left. This is the only way to do it. (This reminds us of the second step in the 7-clue puzzle) 6-3

Then the solution follows.

Improve this answer
$\endgroup$
4
  • 1
    $\begingroup$ Sorry about the edit. I didn't expect I would find the 6-clue puzzle so soon, and I didn't feel like posting a separate puzzle for that. $\endgroup$
    – Bubbler
    Commented May 22 at 2:24
  • $\begingroup$ No problem! Thank you for the nice puzzles :) $\endgroup$
    – Benjamin Wang
    Commented May 22 at 2:56
  • $\begingroup$ In the 6-clue puzzle, I am not clear on why the 13 must go where you put it as an "obvious" deduction. It seems to me it could be 1 to the left (at that stage) and still connect. $\endgroup$
    – Matthieu M.
    Commented May 22 at 14:23
  • 1
    $\begingroup$ @MatthieuM. Thank you for noticing it. I must have gone back and forth in my solve and took screenshots at inconsistent times. I have now fixed the solve path to be more logical. $\endgroup$
    – Benjamin Wang
    Commented May 22 at 15:51
2
$\begingroup$

Here is an image with the solution to the 6 clue puzzle:

enter image description here

Improve this answer
$\endgroup$
1
  • 2
    $\begingroup$ Whoa you beat me by 39 seconds but luckily we solved different puzzles. Seeing this, I'll work on writing out my solve paths instead of re-doing your solution. $\endgroup$
    – Benjamin Wang
    Commented May 22 at 2:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.