# Minimally clued 4x5 Hidato (4 clues)

:)

### Background

So as you might or might not know, I have been studying the minimum number of clues needed to force a unique solution in Hidato for variously sized boards. I recently had come up with a 5x5 Hidato with 5 clues, although it was found to have multiple solutions.

Yesterday, @Bubbler was able to find a 5x5 Hidato puzzle that had 4 clues while having a unique solution, and 14 hours ago, they also found a 5x5 Hidato puzzle with a unique solution and only single-digit clues.

This morning, I managed to create a 4x5 Hidato puzzle again with 4 clues, which I verified to have a unique solution first by hand and then through @Bubbler's Picat program. Can you figure out the solution?

### The puzzle

Goal of Hidato:

Fill in a grid with a series of consecutive numbers that connect each other orthogonally or diagonally

To get the green checkmark $$\color{green}✓$$:

Solve the following Hidato puzzle

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


First, fill in the 19 (there is only one solution which reaches 16)

     1  .  .  .  .
16 .  .  .  .
.  .  .  19 .
.  .  .  5  20


Then, fill in the 18 and the 17 in order to avoid cutting apart the 1 and the 5 or hemming in the 16

     1  17 .  .  .
16 .  18 .  .
.  .  .  19 .
.  .  .  5  20


Then, we need the diagonal between 18 and 19 to give the 16 a path to escape, so we can fill in the 3 and the 4

     1  17 .  .  .
16 2  18 .  .
.  3  .  19 .
.  .  4  5  20


Using numbers with only one empty neighbor:

     1  17 .  .  .
16 2  18 11 7
15 3  12 19 6
14 13 4  5  20


There is obviously only one solution for the final three numbers.

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