25
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For an example of how this type of puzzle works, see here...


I believe I have invented another new type of puzzle...

What is its name?

enter image description here

Colour-blind-friendly version available here.

Begin by solving the 9x9 sudoku; each of the digits 1-9 must appear exactly once in each row, column and thick-bordered 3x3 box. Then apply some (!) and discover its name!

Hint:

Its name is 8 letters long. Though you may be able to guess it, you'll need to explain how to derive it from the puzzle...

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The name of this puzzle is

Yajidoku

I solved the Sudoku, then learned from the other answers here, that the next step is to solve a Yajilin, a puzzle type I haven't heard of before. As these both steps are already covered in the other answers, I only give the combined solution here:

Yajdoku

Now the last step is

to sum up in each of the nine Sudoku blocks both the numbers colored initially and the numbers blackend for the Yajilin. The middle block has no such numbers, the other sums are, read clockwise (like the arrows indicate) starting top left*:
25, 1, 10, 9, 4, 15, 11, 21
mapping this on 1-26 = a-z gives:
YAJIDOKU

*Addition:

If we order the colours as they appear in the rainbow from the outside to the inside, we have red - yellow - green - blue, which hints to start reading top left.

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  • $\begingroup$ Well done - I’d been wondering about this for a while! Very clever solution :) $\endgroup$ – Avi Jan 14 at 0:25
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    $\begingroup$ sweet lord this is complex D: $\endgroup$ – Adib Jan 14 at 2:22
  • $\begingroup$ Brilliant - well done :) You've nailed down everything except one very subtle hint about why you would start reading from top left (hint: colour). But that part is the most minor of all, so the checkmark is yours! Thanks for completing my puzzle! $\endgroup$ – Stiv Jan 14 at 8:12
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    $\begingroup$ Thank you! It's a great puzzle, too. I guess it's not easy to come from the idea to an actual puzzle. I wonder if the hint for the start point of the last step has something to do with the wavelength of the colours... $\endgroup$ – formica Jan 14 at 23:29
  • $\begingroup$ @formica It definitely does, although there's a very simple way to express that without any science more complicated than a 3-year old would know :) Suffice to say that my colour choices were Not Offhand And Haphazard... $\endgroup$ – Stiv Jan 16 at 7:58
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Partial. Finished the second puzzle, not sure how to read the name of the puzzle from it.

I have solved both the sudoku and Yajilin alone, although the idea of transforming the grid into a Yajilin is jafe's idea. The solution to the Yajilin is the solved Yajilin

Worked Solution.

First, fill in any dead ends. The 4↓ and 3↑ have just one possible solution, and given that there must be a path adjacent to black squares, four portions of the loop can be filled in. step 1
It is impossible for the two highlighted squares to both be black (as they share an edge), and if just one was black, it would create a dead end. Hence neither are black. Also, some other portions of the path have been filled in. The portion to the right of the 1↑ must be filled due to the 2↓ have already been completed. step 2
NB: As Stiv quite rightly points out, darkening only the right-hand square cannot be quite so succinctly eliminated. Luckily, it leads through to this position, from which it can be easily seen to be impossible. This is because the 2← requires an additional square. It must be the one on the right so as to not create a dead end for one of the three 'threads' in that region. However, placing it on the right leads to inevitably creating two distinct loops. step 2b The left-most 1→ has been filled, so the track can be partially identified along that row. Also, consider the 2→ along the bottom row. It is impossible for both black squares due to this 2→ to be to the left of the 1↑ (since that would result in a dead end), so there must be one square to the right of the 1↑. This area can thus be filled in. step 3
The black square of the highlighted 1↓ must be at the top (since one below that would result in two adjacent black squares, and the one below that would violate the left-most 1→). More portions of the track can be easily completed. step 4
Suppose the highlighted square is black. Then the grid must be completed as shown in grey, which will inevitably contradict one of the clues (probably the 1→). This is a contradiction, so the highlighted square is not black. step 5
The squares featuring dots must contain a track (rather than a black square), which allows us to confirm the black square for the 1↑. step 6
The path cannot follow the highlighted direction, as that would create two disjoint loops. We can thus connect the two sections of the track. step 7
The remainder of the puzzle is trivial. step 8

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    $\begingroup$ I love this step-by-step write-up, but I'm not convinced the second logical step is totally sound - at this stage you could shade the right-hand yellow box and still avoid a dead-end by drawing a line down from the left-hand yellow box and another from it heading left to link up to the top line. Do you see? Well done on solving this part though - good progress! $\endgroup$ – Stiv Jan 8 at 7:53
  • $\begingroup$ @Stiv And therein lies the issue with doing a write-up after you've already finished the puzzle. Well, it should be fixed now. $\endgroup$ – ZanyG Jan 8 at 10:03
  • $\begingroup$ Thanks. To be honest, I'm not totally sure that two distinct loops are entirely inevitable here, but following through your what-if-the-right-hand-box-is-shaded logic certainly will result in being unable to fill the bottom two rows whilst satisfying all the criteria, so it still works out... Now can you work out how to derive the name...? $\endgroup$ – Stiv Jan 8 at 10:34
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This is just a work in progress.

The Sudoku looks like this:

enter image description here

That means the colored numbers are:

Red: 2, 1, 1, 2
Yellow: 4, 1, 1, 2
Blue: 1, 3
Green: 2

The surrounding colors looks

a bit like arrows, surrounding the Sudoku.

I have yet to figure out the significance of those numbers, but I'm working on it.


The colored numbers could be placed like this (according to their relative positions):

enter image description here

The positions of the red and yellow numbers are the only options, while the blue and green was chosen at random. I don't know what to make of it though...


Or, as Jafe and Skynet_0 noted, more likely, it's a

Yajilin puzzle. I haven't had time to solve it yet. enter image description here

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    $\begingroup$ Nice! rot13(Vs lbh chg gur pbeerfcbaqvat neebj arkg gb gur ahzore va rnpu pbybherq fdhner, vg ybbxf yvxr n Lnwvyva chmmyr.) $\endgroup$ – jafe Jan 7 at 8:39
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    $\begingroup$ rot13(ybbxf yvxr n lnvwvyva ohg pna'g irevsl fbyinovyvgl / havdhrarff ngz) $\endgroup$ – Skynet_0 Jan 7 at 8:40
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    $\begingroup$ rot13(Urer vf gur lnwvyva. Gur fbyhgvba vf havdhr.) $\endgroup$ – Kruga Jan 7 at 8:58
  • $\begingroup$ Keep going! You're edging closer to the solution... $\endgroup$ – Stiv Jan 7 at 9:18
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Sudoku (solved independently)

enter image description here

Next step (credits to @jafe in CG’s answer’s comments)

Colour > arrows > solve as yajilin

Yajilin

enter image description here (two shaded numbers in bottom are 5s)

Numbers shaded:

7156749358554 from top left to bottom right. Not sure what to do next

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    $\begingroup$ Almost - but your solution doesn't satisfy the green square as it stands... :) $\endgroup$ – Stiv Jan 7 at 9:19

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