# This new puzzle type needs a name {5}

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

What is its name?

Colour-blind-friendly version available here.

Begin by solving the 9x9 sudoku; each of the 9 symbols /, *, +, -, =, ^, >, v and < must appear exactly once in each row, column and thick-bordered 3x3 box. Then apply some (!) and discover its name!

Hint 1:

Every colour used in this puzzle is there to help you solve it, whether for deriving and solving the second-stage grid-deduction puzzle or deriving its name. Every colour...

Hint 2:

then then

Other puzzles in the 'This new puzzle type needs a name' theme: 01, 02, 03, 04

• I think it's time for another hint Commented Feb 22, 2020 at 21:28

First...

... solve the Sudoku, as instructed.

Credit to dcfyj and Kevin Cruijssen for solving this step first.

The completed grid, as depicted by Kevin Cruijssen, looks like this:

Next...

... solve the 5x5 Futoshiki puzzle formed by the white squares and the red-circle inequality symbols between them.

The finished grid looks like this:

Finally...

... we apply the color-coded arithmetic symbols to each row and column. There are four symbols in each row/column (plus an equals sign), which fits perfectly!

Standard order of operations apply. The completed grid reveals our answer.

The new puzzle type's name is...

SUDOSHIKI.

Great construction, Stiv!

• Great job at wrapping this up, mbingo :) Could you include the sudoku image from the comment by @KevinCruijssen (with credit, of course) at the start of your answer for completeness? That would make for a nice comprehensive solution... Then the checkmark will be yours! Thanks :)
– Stiv
Commented Feb 24, 2020 at 15:18
• Done! And again, excellent puzzle (and series)! Commented Feb 24, 2020 at 15:30
• Brilliant, thanks mbingo. I figured Kevin's great diagram needed to be given some 'airtime' rather than being hidden away in the comments. This rounds it off nicely. Have a checkmark!
– Stiv
Commented Feb 24, 2020 at 15:35
• How are you fill color slots after the first step?
– Nick
Commented Aug 25, 2020 at 0:19
• Hi @Nick - the symbols in the grid are the ones which result from solving the sudoku (using the symbols instead of numbers 1-9). You then fill the coloured patches around the outside with the symbols from the corresponding region of the same shape & colour within the grid. Hope that helps! :)
– Stiv
Commented Aug 25, 2020 at 8:56

Partial Solution:

Here's the Sudoku solved

So far I'm not really seeing any viable paths using both the colors and the solved Sudoku symbols. I do see that red

only uses > < V for its symbols.

Which I find interesting, but I'm not sure how to use it. Also, because of the first hint I noticed that

every color clue rests on a gray line, which implies to me that they all should, but if I use the arrows as viable color slots I have too many options, and if I use the arrows for red highlights only, I have too few for the other colors (provided I only place them on the gray)

Which basically just says, I'm still at a loss lol but at least I feel like I'm making a little progress

• Ah, you beat me to it. Was working on it as well: [spoiler] i.sstatic.net/X983n.png [/spoiler]. ;) Commented Feb 17, 2020 at 18:29
• Oh! thanks for the clue, @KevinCruijssen, I hadn't thought about doing that Commented Feb 17, 2020 at 18:40
• I'd say that finding in your last spoiler (right now) may well be puh-retty relevant... Keep going!
– Stiv
Commented Feb 19, 2020 at 15:52
• @Stiv I figured it was, I'm just not seeing how at the moment. I'll give it a proper look see later today when I have time. Commented Feb 19, 2020 at 18:16