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

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