# New record for minimally clued 5x5 Hidato

CrSb0001 has been studying the minimum number of clues to force a unique solution in Hidato for variously sized boards. They came up with a 5x5 Hidato with 5 clues but it was found that it has multiple solutions.

Goal of Hidato:

Fill in a grid with a series of consecutive numbers that connect each other horizontally, vertically, or diagonally.

I was able to find a 5x5 Hidato puzzle with just 4 clues having a unique solution. This was verified with a Picat program (the instance is replaced with a 4x4 one to avoid spoilers; you're free to experiment with the program). Can you find one?

     .  .  .  5  .
.  .  .  .  .
.  .  7  .  .
2  . 19  .  .
.  .  .  .  .


with verified unique solution

    11 10  9  5 25
12  8  4  6 24
13  3  7 18 23
2 14 19 17 22
1 15 16 20 21


• This is solvable by hand. Commented Mar 9 at 4:47

It can actually be done with 3:

     .  .  .  6  .
.  .  .  . 13
.  .  .  .  .
9  .  .  .  .
.  .  .  .  .


with verified unique solution

     1  2  3  6  5
22 21  7  4 13
23  8 20 12 14
9 24 11 19 15
25 10 18 17 16


• This is so good I forgive you for blatantly stealing my post layout ;-) Commented Mar 8 at 8:52
• @loopywalt I don't know what you are talking about =-P Commented Mar 8 at 8:55
• All 3 numbers 1 lower also seems to work Commented Mar 8 at 9:54
• @Retudin the program linked in OP finds 3 solutions, then. Commented Mar 8 at 10:37
• Great job! This is solvable by hand but very hard. Commented Mar 9 at 5:25

     .  .  .  4  .
.  .  .  .  .
.  .  6  .  .
1  . 19  .  .
.  .  .  .  .


Also works as well as its mirror image

     .  4  .  .  .
.  .  .  .  .
.  .  6  .  .
.  . 19  .  1
.  .  .  .  .


Both with unique solutions:

     25   4   8   9  10
24   5   3   7  11
23  18   6   2  12
22  17  19  13   1
21  20  16  15  14


and

     10   9   8   4  25
11   7   3   5  24
12   2   6  18  23
1  13  19  17  22
14  15  16  20  21


and in that logic there should be plenty more in a similar manner where mirror solutions also work. I haven't found any with 3 clues since (I think) you can't force a wall with a gap with only 3 if that makes sense. I'm unsure if the positions (where they are now) are vital to forming the wall with the gap though.

• I would expect, given the nature of the puzzle, that horizontal and vertical symmetries both always apply, no? Commented Mar 7 at 13:40
• ... and rotations too. I would not consider those to be different puzzles/solutions. Commented Mar 7 at 13:48
• True, both symmetries apply as well as rotations of solutions since the direction of execution would simply be mirrored/rotated as well. I don't mind taking the mirror "solution" away @JaapScherphuis I just figured people could still have those puzzles as "unique" too. Commented Mar 7 at 14:09
• You also can reverse the numbers, i.e. apply n -> (26-n). That would be less obvious. Commented Mar 7 at 20:40