Sudoku like you've never seen it before

I've spent this week trying to create a difficult logic puzzle which is a combination of two Sudoku varaints, 'Samuari Sudokus' and 'Pseudokus', and this combo is unlike anything you can find online. The rules are under the puzzle.

Solving it myself when double checking took my quite a while, but was fun so hopefully this will be enjoyable!

$$\huge\text{SAMURAI PSEUDOKU}$$

RULES:

• There are 9 individual grids, which overlap. The 9 grids obey normal Sudoku rules. The outline of each individual Sudoku is marked by a thick black line.

• The overlap between two grids is the same. I.e. the cells in overlapping boxes obey the rules of both of the two sudokus.
• The grey squares indicate where no grids overlap and where the cells don't contain any digits.

• All the numbers given ($$\color{red}{\text{in red}}$$) are either 1 more or 1 less than the actual digit for that cell. I.e a $$\color{red}{4}$$ could either be a $$3$$ or a $$5$$ and so on.

• To clarify as well, there is no wrap around. A $$9$$ cannot give a $$1$$ and vice versa.
• There is a single solution that can be deduced logically with no guesses.

A full solution will be accepted with

• A complete grid
• At least a little bit of explanation (preferably with some images) e.g. where you started, route you took etc.
• If possible, the time it took you to solve! This is just for my personal interest :)

Enjoy!!!

A new Sudoku variant - Sudoku in the third dimension (3D Sudoku)

• Must... resist...! Save... my weekend...! – Stiv Aug 7 '20 at 18:13
• @SteveV yes all numbers given (in red) are one off – Beastly Gerbil Aug 7 '20 at 18:13
• @JeremyDover well, I don't think 0 or 10 are allowed in Sudoku ;) – Beastly Gerbil Aug 7 '20 at 18:27
• @JeremyDover I assume that can only be a reference to "This Is Spinal Tap - The Sudoku" from Cracking The Cryptic :-) – happystar Aug 7 '20 at 22:10
• @bobble Dw this is supposed to be hard! It took my parents 6+ hours to solve and me about 3, and that’s with my knowing how the puzzle works!!! – Beastly Gerbil Aug 7 '20 at 22:57

This seems to fit:

The initial step was to replace all 1's (red) with a 2 (black) and all 9's with an 8:

Then, whenever a red number was +/- 1 of a black number which was on the same row, column or box, the red number was changed to its other possible value. E.g. if a red 6 was on the same row as a black 5, the red 6 was changed to a black 7 as it couldn't have a value of 5. A snapshot of this (concentrating on the central Pseudoko) is here:

I then continued this process, using normal sudoku techniques as well. As there were only even black numbers to work with, I only replaced odd red numbers. Below is as far as I got this way:

In retrospect it was a mistake to not try replacing even red numbers as well, as I would need to do this eventually anyway and replacing them could provide additional information. Below is a snapshot after I started this process:

My first completed part-sudoku:

After this I completed each part-sudoku, one by one, until all were done.

Took about 5 hours all told.

An amazing new version of Sudoku! Should become a new stable in my view.

• Well done Jens :) I was only 30 minutes in, so you've spared me a lot of disappointment and heartache by posting now! (Would love to know how many others were also mid-solve...!) – Stiv Aug 8 '20 at 13:17
• @Stiv Thanks! Glad I could help ;-) – Jens Aug 8 '20 at 13:36
• me @Stiv XD gj jens and +1 – Omega Krypton Aug 8 '20 at 13:56
• Well done Jens!!! This looks right, I’ll double check when I get home. I also find it interesting the path you took, I solved the middle sudoku first :) I’ve been asked to make a ‘the making of’ so I’ll explain that a bit more there. Very well done though! 5 hours is a lot less than I was expecting :) hopefully it was enjoyable!! Planning to make more sudoku variants in the future – Beastly Gerbil Aug 8 '20 at 17:34
• @Beastly It was very enjoyable! I thought I got a late start and was resigned to not posting first, but continued just for the fun of it. I was a bit amazed when no one had posted when I finished. A small quibble is that after solving the first 4-5 part-sudokus it was starting to become a chore to finish the rest. Smaller is sometimes better ;-) – Jens Aug 8 '20 at 18:07

I have been asked by a couple of people to show the creation process for this puzzle, so here we go:

Also if people want to see more of these strange, Sudoku mash ups then I'll be more than happy to combine some new types :)

Wrap-up: The Making Of This Samurai Pseudoku

This is not a solution to the puzzle, but provides notes from its poster. This type of answer has been approved by the community.

Caution: This post contains spoilers.

Inspiration

A big source of inspiration was from a place a lot of you might recognise, the youtube channel Cracking the Cryptic, which involves two world class sudoku solvers taking on the hardest and most clever sudokus around.

The majority of these sudokus are not standard, and involve certain gimmicks, the most common being things like a knight's move constraint, thermometers, no consecutive digits and so on. These new constraints force the solver to think about the new sort of logic that can be applied to the puzzle.

These puzzles really interested me, and having done lots of tough, but normal sudokus I set out looking for apps for my phone that had sudoku variants. This was harder than I thought but I eventually stumbled upon an app called Sudoku Mega Bundle which was exactly what I was looking for.

This app has 125 different Sudoku variations, which is unbelievable for a free app. There is a 'random puzzle' button, and I started trying out as many different puzzle types as possible. There's still many I haven't even looked at yet!

Anyways, I instantly fell in love with 'Pseudoku' which I found super fun and clever, and a whole new type of logic. It was at this point I started wanting to make my own, and I thought a simple 9x9 would be interesting, but rather trivial for the site. I wanted to make a sudoku that had never been seen before, that was difficult, that would provide a challenge.

I had already stumbled across 'Samurai Sudoku' - which wasn't my favourite, but I realised it would work very well with 'Pseudoku'. A larger puzzle would also be much harder that a simple 9x9 (there is over 600 cells in this puzzle compared to just 81!!) so I set my mind on this and started to make one.

Creation (and resources)

Starting off

For resources, all I used to create this was Excel. It's a nice simple place to work with cell based puzzles. I also used Sudoku-solutions to check my sudokus were valid along the way.

To begin with, I designed the grid. For added aesthetics, I added grey and black around it, and also added a border of 'PSEUDOKUSX9' around the edge. Towards the end I realised that 'PSE' was in there so I made that red just for the site.

After adding the borders in for each sudoku, I realised that it looked slightly confusing, so added thick borders around the edge of each sudoku. I think this has helped a bit, however it is still rather confusing to look at.

At this point I had an empty grid that looked like this:

Creating a solution

From here I needed to create an intended solution. At this point, all the sudoku had to do was obey normal sudoku rules, and I just had to be careful with the overlaps.

It is relatively straightforward to create a sudoku solution, I drew a 9x9 grid and created the first one. To do so, I filled in all the $$1$$s making sure they obeyed sudoku rules. Next I filled in all the $$2$$s, again making sure no rules where broken.

From here I filled in the top 3 rows, and then the leftmost 3 columns, and then 3 or 4 extra numbers in the middle. To get a full solution, I would first check with an online solver that there was only 1 solution and then solve it myself. And boom! First solution created.

Here's an example of what I would aim to reach:

I placed this in the topmost grid. From here I moved one to the right, then created that solution using the overlap as a starting point. After creating that, I realised the middle would be quite important so filled that in. I was careful however, as the topmost grid added some more restrictions into what I could make the top left box of the middle grid.

After this I went round clockwise until the whole grid was filled. For the majority of the grids, certain boxes would overlap and as a result there were added restrictions for certain boxes that you just had to watch out for.

I did make one error; when creating the bottom grid, I forgot to include the added restriction for the top left box from the bottom right box of the center, but luckily realised before I went any further.

I now had created the whole grid:

Creating the clues

This was where it was going to get tricky however. I now had to remove clues such that it was solvable, while at the same time making it hard as possible, while also introducing the 'Pseudoku' numbers.

I copied the grid, and emptied it so I had the following set up (but at this point both of the grids to the right were blank):

This is where it got interesting, and where I imagine most are interested to see how I made this.

The left grid was the solution I wanted, the middle grid was the clues given that I was filling in, and I used the rightmost grid as a 'what can be solved using the clues I've put in so far' grid.

Basically the right grid was used to solve as I went along filling the middle grid in with clues. The left grid was for reference.

I started to fill clues in for the middle grid. I placed a few $$1$$s and $$9$$s where there were $$2$$s and $$8$$s as this was an easy place to start, but didn't want to put too many in.

When I found 'Psuedoku' - I also discovered some interesting logic. 2 of the same number in a row/column/box will mean that any clue 2 more than those numbers can be resolved.

For instance, two $$5$$s in a row will mean a $$7$$ MUST be an $$8$$, as one of the $$5$$s MUST be a $$6$$ and therefore the $$7$$ cannot be. This was the basic logic I wanted to use to make this puzzle solvable, and a key piece of logic for Pseudokus.

I also decided that, as much as possible, I wanted a grid on it's own to be insolvable without knowledge from overlapping grids. So when filling in clues, I also filled in a few numbers on surround grids that would mean a number could be fixed in the corresponding overlapping box.

I repeated this process until there were enough clues for the centre to be solved. The logic required would be a mixture of

• normal sudoku logic
• smallest/largest number logic ($$1$$ must be $$2$$, $$9$$ must be $$8$$)
• double number logic ($$5$$, $$5$$, $$7$$ means $$7$$ must be $$8$$)
• logic from surrounding cells

From here I continued this process for other grids. I tried to make sure to fill in as few clues as possible, while also making sure that surrounding grids were needed to help solve a new grid.

The hardest to clue where the boxes on the outside where there was no overlap. For many, I had to put more clues than I would have liked, but as there is no overlap, no knowledge from other cells could be used to help resolve numbers.

I kept going, solving as I went using the right hand grid until I was fairly confident that there were enough clues to solve the grid.

Double Checking

At this point I had spent DAYS creating this puzzle. I wasn't about to post it in a hurry to find out there was a mistake or that there wasn't a solution!

I double checked this puzzle in two ways, checking the clues, and checking the puzzle.

Checking the clues

Firstly, I wanted to double check that my 'solve-as-you-go' solution was correct. I created another blank grid, and wrote the following into the top left cell:

'=A1-Z1'

where the actual cell numbers where the top left cell of the solution, and the top left cell of my go-along solution.

Dragging the formula across the grid, I got a number showing the difference between my intended solution and my go-along solution for each corresponding cell. Luckily for me, the whole grid was all $$0$$s, meaning my solution matched the intended one!!

Next I wanted to check the clues were all one more or one less than the solution number. However, I didn't want to just calculate the difference for every cell, as I don't care about the difference if the clue cell is blank. For the same grid, I wrote the following into the top left cell:

'=IF(A1 = 0, '', ABS(A1-Z1))'

where the actual cell numbers where the top left cell of the solution, and the top left cell of my clues. This formula meant that the difference would only be displayed if the clue cell wasn't blank.

Once again, luckily for me, all the cells showed a $$1$$, meaning all my clues were correct!!

Checking the puzzle

The only real way to check the puzzle was solvable was to solve it myself. At this point my parents were also interested in my creation, so I printed off copies for them too.

It took me about 3 hours to solve in total, but that was me knowing the logic and knowing the rough solving route that is easiest. It took both my parents 6+ hours, but we all managed to solve it, and all managed to get the correct solution so I knew my puzzle was solvable. The time taken also meant I knew it was quite hard, which is exactly what I wanted!!

I copied it to both google docs and to drive so it could be downloaded, clipped the clues and the puzzle in front of you was the result!

Takeaway

Some things I've taken from creating this puzzle:

• Don't create tough logic puzzles when tired - seriously, you'll make mistakes. It's better to wait till the next day when you're thinking clearly. It will save you in the long run.

• You can never have enough double checking - for larger complex puzzles, a small error could set you back hours. Double checking as you go as well as after creation is invaluable to all complex puzzles.

• People enjoy new things! - for puzzle creators, the best received puzzles are always those that come up with new concepts. Even if it's simply a new type of sudoku!

• Clarify what the rules/instructions - your instructions need to be clear. I originally left out the fact that there was no 'wrap-around' so it could be a $$9$$ could clue an $$8$$ or a $$1$$. This puzzle probably wouldn't be solvable if true, so make sure that people know what you mean!

I hope this was an enjoyable puzzle, and if anyone wants to see some new variant mash ups please let me know!

If anyone has some more questions feel free to ask :)

With that, this was how this puzzle was created! Hopefully you can take something away from this post. Thank you all for solving!

• Thanks for posting this! It looks like it really tooks lots of work to make this, even more than just plain solving the puzzle (which I assume is the case most of the time). Seeing the process of how a large puzzle like this is made (and the stuff you learned while making it) have given me more motivate to work on larger and more complex puzzles :D – thesilican Aug 8 '20 at 22:14
• Great to gain an insight into the process behind this puzzle :) It's clear from the write-up that this was a monumental effort on your part. I for one am glad you persevered... Fantastic new puzzle! – Stiv Aug 8 '20 at 22:14
• @MrSiliconGuy it would be great to have more people making things like these! :) Glad this helped, and it certainly took a lot of time :P – Beastly Gerbil Aug 8 '20 at 22:21
• @Stiv thank you! I'm just surprised you didn't solve it first :P Certainly was a lot of effort, but honestly the most important thing was taking my time. I think if I had found out I had made an error at the end I would have completely abandoned this so going a bit slower and over-checking was definitely worth it and to some degree I got lucky that I managed to get it all correct first time :) – Beastly Gerbil Aug 8 '20 at 22:23
• Ha! I'm afraid I had a busy weekend! :) Taking your time to test a puzzle is so key - there is never a need to rush to publish on PSE, and that's an ethos that really needs to be emphasised to wannabe puzzle setters. Take your time and create something great :) Thanks again! – Stiv Aug 8 '20 at 22:30