A 6x6 table with nothing filled out?

Question

So as you might or might not know, I can be quite evil sometimes, especially with my Hidato puzzles that contain no numbers.

But, today, I decided to give you an enigmatic-puzzle! This means that you will have to determine what type of puzzle this is and solve it completely. However, you do have this to help you:

$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$
$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$
$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$
$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$
$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$
$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$	$\color{white}.$

R1: roobbo
R2: robobb
R3: brybro
R4: yooyrb
R5: bbobbb
R6: boborg

Hint 1:

The lowercase letters (except b) represent colors, but what do the colors represent?

Hint 2:

Look at the tags.

Answer 1

The completed grid:

Where do we start?

Adding the colours to the grid gives us the following:


First I guessed that this would probably be another coloured Hidato puzzle, similar to some of your recent puzzles.

Hopefully this puzzle works in the same way (place the numbers 1-36 in the cells of the grid, so that consecutive numbers are adjacent (orthogonally or diagonally)). So we need to work out what the different colours represent, and then solve the puzzle.

There are six red cells, which matches the number of square numbers in range (1, 4, 9, 16, 25, 36).

There are eleven orange cells, which matches the number of primes in range (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31).

There are three yellow cells and (based on previous puzzles) these could be the remaining Fibonacci numbers not already covered by earlier sets (8, 21, 34).

And finally there is a single green cell. This could be several things, but (again based on previous puzzles) this could be the single cube in range that is not already covered (27).

Let's start solving:

We need a connected sequence of red-orange-orange-red-orange for 1-2-3-4-5. There are only two ways to place 1-2-3-4 (with another orange cell adjacent for 5), and one of them completely isolates the top-left cell. So we can place 1-4.

In the opposite corner, 27 goes in the single green cell.

29 must in an orange cell two cells away and there is only one possibility.

28 must be in a white cell between those two.

and then 26 must be in the remaining white cell adjacent to 27.

The red cell below the 1 cannot be 5 (orange), so is a dead-end. That means it must be the other end of our number chain, and 36 works.

35 is then forced and 34 must be in the yellow cell below that.

In the bottom right, we have another red cell has only one free neighbour. We cannot have another dead-end, so it must join to the existing chain, so must be 25.

And then 24 is forced.

8 must be in a yellow cell, and have a red neighbour for 9. So we can place 8 and 21.

There is only one way to place 22, 23 (white,orange) to join up 21 and 24.

That forces 20 (white)

And 5 and 7 (both orange).

And then 6 (white) must join those.

Now the path from 29 to 34 in the bottom left is forced.

Orange cells (primes) cannot contain consecutive numbers (except for 2 and 3 which are already placed). The orange cell above the 20 only has one free non-orange neighbour, so must join to 20. So that is 19.

That forces 18, 17, 16 (white, orange, red).

And that leaves no choices for 9, 10, 11.

Finally, 13 must be in the single remaining orange cell.

And from here, there are unfortunately two ways to complete the chain from 11 to 16: