*Hi,*

[Our company] has just launched [another crappy app] - which is an unique Sudoku app for the iPhone. The way it differentiates from all other Sudoku games is the fact that it is three dimensional and brings in an unique combination of fun of spinning dials and sliding pieces with number puzzle.

We noticed that you have been writing about other Sudoku puzzles and thought this app would be of interest to you. We would request you to write a review for this app for your readers. You can download the app for Free at [link to the "Pro" version of the app that costs money, as opposed to the free demo version].

For your convenience we have also attached with this email the official press release and the screen shots of the app along with this email.

In case you need any other information to publish a review for [another crappy app], we will be glad to help you with the same.

[Our company] has just launched [another crappy app] - which is an unique Sudoku app for the iPhone. The way it differentiates from all other Sudoku games is the fact that it is three dimensional and brings in an unique combination of fun of spinning dials and sliding pieces with number puzzle.

We noticed that you have been writing about other Sudoku puzzles and thought this app would be of interest to you. We would request you to write a review for this app for your readers. You can download the app for Free at [link to the "Pro" version of the app that costs money, as opposed to the free demo version].

For your convenience we have also attached with this email the official press release and the screen shots of the app along with this email.

In case you need any other information to publish a review for [another crappy app], we will be glad to help you with the same.

I may need to rename "Grant's Review Corner" "Grant's Annoyed Rant Corner".

Research indicates that [another crappy app] is an adaptation of a physical puzzle that markets itself as follows:

*[Crappy thing] puzzle starts where a traditional Sudoku puzzle leaves off...*

...at the solution. We took a completed Sudoku solution, and wrapped it around a three-dimensional cylinder. Then we divided the cylinder into nine independent layers. The challenge of the puzzle is to take those 9 layers of the cylinder, and orient them correctly, horizontally and vertically, so that you have re-created a Sudoku solution. That means that each row, column, and block contain each of the numbers 1 through 9, only once.

The logic of the [crappy thing] puzzle is very similar to what you would use to solve a traditional Sudoku. Based on the numbers that you know, what are the remaining possibilities. In our case, however, there are no numbers to fill in, you just have to order the pieces correctly, so that it produces a Sudoku solution.

The puzzle has over 300 possible solutions, the challenge is finding one of them!

...at the solution. We took a completed Sudoku solution, and wrapped it around a three-dimensional cylinder. Then we divided the cylinder into nine independent layers. The challenge of the puzzle is to take those 9 layers of the cylinder, and orient them correctly, horizontally and vertically, so that you have re-created a Sudoku solution. That means that each row, column, and block contain each of the numbers 1 through 9, only once.

The logic of the [crappy thing] puzzle is very similar to what you would use to solve a traditional Sudoku. Based on the numbers that you know, what are the remaining possibilities. In our case, however, there are no numbers to fill in, you just have to order the pieces correctly, so that it produces a Sudoku solution.

The puzzle has over 300 possible solutions, the challenge is finding one of them!

Over 300 solutions, huh? Well, on A Cleverly-Titled Logic Puzzle Blog, I only deal with puzzles with exactly

*one*solution, so already I can tell that your app, which is essentially 10,000 different [crappy thing] puzzles for the price of one iPhone app and which advertises "1200 different solutions for each puzzle", is beyond the scope of this blog. But let's give your puzzle a try, shall we? I've been pleasantly surprised before by puzzles that seem like they'll be nothing but tedious trial and error (like IcoSoku, a toy which I got for Christmas from my parents and found easier and more enjoyable to solve than I expected).

The following puzzle is not taken from the game, but was generated using a method which I suspect to be similar to that which generated the 10,000 puzzles in the app:

125798436

129358476

132798645

135962847

139564827

167392548

165397824

173924658

195428367

The most promising strategy I see for tackling this puzzle is to focus on the Latin square aspects of the puzzle first (orienting the rings so each number appears once per row and column), and then focus on the 3x3 boxes. I will consider one ring at a time, looking at every possible orientation of that ring and seeing if any of them can be added to the puzzle thus far.

The first ring is fixed:

125798436

The second ring can be added in four ways:

125798436 125798436 125798436 125798436

612935847 476129358 293584761 358476129

The third ring increases the possibilities to six:

125798436 125798436 125798436 125798436 125798436 125798436

612935847 476129358 293584761 358476129 612935847 476129358

279864513 798645132 986451327 279864513 864513279 864513279

And so on and so on.

125798436 125798436 125798436

358476129 612935847 612935847

279864513 864513279 864513279

847135962 471359628 596284713

125798436

612935847

864513279

471359628

956482713

125798436

612935847

864513279

471359628

956482713

548167392

125798436

612935847

864513279

471359628

956482713

548167392

397824165

125798436

612935847

864513279

471359628

956482713

548167392

397824165

739246581

125798436

612935847

864513279

471359628

956482713

548167392

397824165

739246581

283671954

Okay, I'm honestly a little surprised there. The first couple rings caused the possibilities to branch out, but rings four and five killed possibilities, and from that point on, only one possibility ever existed. It could have been much more tedious.

Next step is to arrange the rings into a Sudoku puzzle where the 3x3 boxes all contain each of the numbers exactly once. Keep in mind that not only can the order of the 9 rings be changed, but the vertical dividers between the 3x3 boxes can be positioned in 3 ways (equivalently, the whole puzzle can be rotated 1/9 of a rotation left or right in respect to the vertical dividers). Assuming the vertical dividers split the first ring 125/798/436, are there two rings that, in combination with this ring, create a valid Sudoku box with the 125? It is simple to check every ring in combination with the first ring to see if the numbers don't duplicate, and if another ring will complete the box. It turns out that 864/513/279 and either 397/824/165 or 739/246/581 will do so; of these, only 739/246/581 completes all three boxes. Similar checking shows that 257/984/361 and 579/843/612 do not yield any possibilities. The remaining 6 rings can then be divided up in one way. Excluding trivial transformations such as changing the order of the three groups of rings, changing the order of rings in a group, or rotating the puzzle by 1/3 of a turn, the only solution is as follows:

125|798|436

739|246|581

864|513|279

---+---+---

283|671|954

471|359|628

956|482|713

---+---+---

397|824|165

548|167|392

612|935|847

Note that if you account for trivial transformations, then every solution has 3!*3!*3!*3!*3=3888 variations. Where did "over 300 possible solutions" and "1200 different solutions for each puzzle" come from? My best guess is that 1200 came from the 1296 solutions a puzzle has if you exclude rotations. But "over 300"? Well, technically, 3888 is over 300, but still.

Now I divulge how I created this puzzle: I took a completed Sudoku solution, wrapped it around a cylinder, and divided it into nine layers. What a surprise.

I quote the above advertising: "The logic of the [crappy thing] puzzle is very similar to what you would use to solve a traditional Sudoku. Based on the numbers that you know, what are the remaining possibilities." The above solving process was nothing like what I'd use to solve a traditional Sudoku, because in a traditional Sudoku, I don't usually need to branch and bound, and can usually fill in numbers because the numbers I already know

*force*something to be true.

Now, to be fair, [another crappy app] does look pretty:

[another crappy app] has a far more polished presentation than [name redacted].

Maybe the puzzle is actually more fun to play by manipulating pieces than by using text like I did above. I know I'd go insane if I tried to find every possible solution to IcoSoku in a text editor, as opposed to just looking for one by playing around with physical pieces. Perhaps I am just using really good tactics, or perhaps there are in fact tons of solutions to one puzzle, making the search for a single one that much easier, but I actually

*like*IcoSoku, somehow. I decided to give [another crappy app] a try; maybe the tactile sensation of using the touch screen would enhance the experience beyond what I experienced above, I thought. Maybe the 10,000 puzzles in the app will enhance the replay value, just as IcoSoku's millions of puzzles and tactile feel enhance its replay value.

Eight puzzles later (it turns out that the free version of the app has all 10,000 puzzles, and only differs from the paid version, from what I can tell, by having advertisements), I came to the conclusion that [another crappy app] is too much like boring rote work and not enough like a puzzle or a game for my pedestrian tastes.

I used the following strategy each and every time:

1) Align all of the 1's in a single column.

2) Without rearranging the rings, iterate the following steps, starting with the second ring:

a) Rotate the ring one step to the left.

b) If the 1 on the current ring aligns with the top ring, apply step 2a on the previous ring.

c) If the current ring conflicts with the above rings, apply step 2a to the current ring.

d) If the current ring does not conflict with the above rings, apply step 2a to the next ring. If this is the last ring, record the order of the numbers in the column with 1 on top and go to step 3.

3) Without actually rotating any rings or moving the top ring, check if the top ring can make valid Sudoku boxes with two other rings. If so, check if valid Sudoku boxes can be made using the other six rings. If so, you have solved the puzzle. Otherwise, pretend the vertical boundaries are 1/9 of a turn to the left, and reapply the process, rotating the rings if a solution is found. If no solution is found, pretend the vertical boundaries are 1/9 of a turn to the right, and reapply the process, rotating the rings if a solution is found. If no solution exists, rearrange the rings according to the order you recorded in step 2d, reset the bottom ring to align the 1 with the 1 on the top ring, and apply step 2a to the second from the bottom ring.

Gyah, I feel like I use my brain more when solving Nikoli's easiest Sudoku puzzles than when solving these. If I wanted to do rote work, I'd volunteer as a page at a library and make sure the books are in proper order by their Dewey decimal numbers -- at least I'm helping the community by doing so, not to mention that I find it relaxingly enjoyable for some reason. [another crappy app] does not look to have similar artistic or logical possibilities to Sudoku, and is therefore not something I can recommend highly. It's a one-off puzzle at the most, not something I'd want to do 10,000 times except for the sake of science.

By the way, ever since I posted my two-star review of [another crappy app] on iTunes, 13 five-star and 11 four-star ratings, all accompanied by reviews, have been posted. Looking at the other apps these users have reviewed, I believe them all to be shills. (In particular, virtually all of the five-star reviewers have also reviewed "Pay Anywhere - Accept Credit Cards" and "Phone Swipe - Credit Card Terminal", and other apps that seem to be made by the same people.) Yuck!

## 3 comments

Strangely, I never get emails to review things like this. I wonder why that is. - ZM

So, what IS an effective strategy for solving the Icosoku?

Chaos Incarnate: I tend to start with the 2-2-2 and 3-3-3 tiles and the high-numbered vertices, and then just try stuff, with the 1-2-3 tiles being a bit higher in priority.

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