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Previous puzzle

As you may or may not know, I can be a bit evil sometimes. Today, I am going to give you a 5x5 Hidato with no given numbers to start. However, this isn't a Mobius Strip puzzle like last time, and luckily, there are colors to help you! Here is what the colors represent:

  1. $\color{green}{\text{Green}}$ represents that a number is a square number. This includes $1$.
  2. Yellow (not coloring this due to visibility issues) represents that a number is a prime number. (e.g. 2, 3, 5, 7)
  3. $\color{red}{\text{Red}}$ represents that a number is a multiple of $6$. This includes $6$.
  4. Finally, $\color{blue}{\text{blue}}$ represents a number in the Fibonacci sequence that is not already represented by any of the other colors.

However, here's the problem: While there are colors to help you out, you do kinda have to solve a Nonogram to start the Hidato.

Rules of Nonogram:

The grid must be colored or left blank according to numbers at the side of the grid to reveal a hidden pixel art-like picture.

Rules of Hidato:

To fill the grid with a series of consecutive numbers adjacent to each other orthogonally or diagonally. All tiles are required to be filled in.

The puzzle:

enter image description here

(sorry for not transcribing the puzzle for colorblind users - I am not sure how to do so for Nonograms with multiple colors)

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  • $\begingroup$ solving the nonogram gives 5 green squares. Therefore 1-25; however there are also black squares where no number is written, leaving 25 too big... $\endgroup$
    – Stevo
    Commented Nov 17, 2023 at 20:46
  • $\begingroup$ @Stevo The black squares aren't needed, that's just for filler $\endgroup$
    – CrSb0001
    Commented Nov 17, 2023 at 21:17
  • $\begingroup$ So its just a 5 by 5 box with different colours including white? $\endgroup$
    – Stevo
    Commented Nov 17, 2023 at 21:27
  • $\begingroup$ @Stevo Yes, that is the case $\endgroup$
    – CrSb0001
    Commented Nov 17, 2023 at 21:28

1 Answer 1

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First we solve the nonogram

enter image description here

There are

five green square numbers in our 5x5 grid so we must be using the numbers 1 through 25.

Then we see that only one of the

two blue Fibonacci numbers is touching a green square number. That must be 8 touching 9. We can fill in a couple neighbors based on color. The other blue Fibonacci number is 21.
enter image description here

Then the two

whites touching 21 are 20 and 22. Two of the three yellow primes touching them must be 19 and 23 and the third must be 5 touching the 6. That means the green cell two cells above the 6 is a 4 and the 3 must be above that, leading to 2 and 1.
enter image description here

Since the yellow

prime to the right of 10 is accounted for, the one above and to the left must be 11, leading us to 12, 13, 14, and 15.
enter image description here

Now the yellow

prime in the top-right can't connect to two green square numbers so it must connect to one green square number and a red multiple of six. That must be 17 touching 16 and 18 (though we can't yet tell which of the two greens is 16). But now we know which of the yellow primes is 19, which leads to 20 and 22.
enter image description here

Finally the red

multiple of six above the yellows must be 24, the green above it 25. Then the green above that must be 16.
enter image description here
The two remaining yellows primes are interchangeably 5 and 23.

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