Fillomino-Fillia Preview Series: Odd-Even Fillomino

This is an odd-even Fillomino (AKA Polyominous). In addition to the usual rules, the odd numbers must form a single polyomino, and the even numbers must similarly form a single polyomino.

Answer entry: Enter the units digits of each square in the marked rows and columns, from left to right for rows and from top to bottom for columns.

Highlight to see the answer: 9142436235 1999913315

Long-time readers may recall the first odd-even Polyominous on this blog, where the odd-even parity of each cell was given from the outset. This incarnation allows the odd numbers and the even numbers to interact more (by which I mean at all).

Fillomino-Fillia Preview Series: Classic Fillomino

This is a classic Fillomino (AKA Polyominous), operating by the classic rules.

Answer entry: Enter the units digits of each square in the marked rows and columns, from left to right for rows and from top to bottom for columns.

Highlight to see the answer: 8887771445 7772272554

You may notice that this image looks different from my usual images. That's because it was created by MellowMelon using a program (although the puzzle represented by the image was, of course, lovingly crafted by yours truly). This is how all of the images will look on the test, meaning you won't be able to tell which puzzles I made and which ones MellowMelon made, drastically increasing the difficulty of the test! (Or. . . not. :) )

Fillomino-Fillia!

In October of 2010, I had my first taste of solving puzzles in a competitive environment, thanks to the 20/10 Puzzle Decathlon, a well-written test by grandmaster Thomas Snyder which was hosted on Logic Masters India. As exciting as the whole experience was, I am even more excited to announce that this coming weekend, as I have hinted at previously, fellow logicsmith Palmer Mebane and I will present Fillomino-Fillia, a test on Logic Masters India consisting entirely of Fillomino puzzles (including a bevy of variations). I hope you will choose to participate in this test.

To participate, you will need to register an account on Logic Masters India. Download the instruction booklet and (when it is made available, which I'm told is usually a day before the test starts) the password-protected puzzle booklet. You may choose to start the test at any time during the weekend of June 4 and June 5 (note that this is GMT, so participants in the US, for example, will have between late June 3 and late June 5 to begin the test). When you do, the password to unlock the puzzle booklet will be given to you, and you will have 120 minutes to print out and solve as many of the 18 puzzles as you can. Each puzzle is worth a varying number of points, roughly corresponding to its difficulty; the harder the puzzle has been judged to be (based on the opinion of the authors and the test-solvers), the more points it's worth. When the 120 minutes have expired, you can see how well you performed, and how you compared to other contenders.

Some words of advice based on my experience:
* Read the freaking instruction booklet. When you're an idiot like me, you have no idea how much having your mind as prepared as possible to the puzzle booklet's contents will help you perform better on the test, until you've made the mistake of starting the test without such preparation.
* Check your answers as you enter them! Improper checking of my answers definitely cost me some points. In particular, I wish that I had notated the grids more than I thought I needed to for the purposes of solving quickly, to make it easier to check my answers.
* Practice! Over the next few days, and in lieu of my usual Monday Mutants post, MellowMelon and I will be posting practice puzzles of the varieties you'll see on the test. (It'll be like having several Monday Mutants instead of just one!) Use them to your advantage to sharpen your mind and to prepare yourself for the test that is to come.

Also check out the LMI forums for more discussion regarding Fillomino-Fillia!

Contest 4 Results: A Cleverly-Titled Birthday Contest

The clock striking midnight on my 24th birthday signals the end of A Cleverly-Titled Birthday Contest. In this contest, solvers were tasked to make geometric order out of a Polyominous grid; when the puzzle is completed, the units digits of the numbers in seven cells can be placed in the blank spots in a URL leading to the AllMusic webpage on a certain song; solvers had to supply the title of the song, or the URL of the webpage. Naturally, now that the contest has ended, my readers, particularly the ones who found time to submit entries, are probably interested in seeing the results.

Warning: the following results contain spoilers (obviously)! If you wish to solve the contest puzzle yourself, please do so before reading on!











I received 56 entries, 53 of which contained the correct answer, either the URL http://www.allmusic.com/song/t1819634 or the song title Subdivisions (by the band Rush). I accepted answers like "1819634", "Subdivisons", and "Subdivided", as well, because I'm nice; however, the answers "All American Boy" [1819234], "At the Dawn of Humanity" [1810634], and "Echo" [1819654] did not conform, and were cast out.

This was quite easily my most spontaneous contest yet on my blog, as there was probably at most a 7-hour gap between conceiving the contest idea and posting it. The inspiration came when I heard the song on the radio during a car ride to church on Wednesday, April 27. I thought, "Huh, interesting. That voice sounds like the guy from Rush. And there are weird time signatures in it, too." I managed to make out enough lyrics to perform a Google search on my iPhone, and discovered what song it was. "Oh, wow, this song is good. I somehow need to create a contest about it." However, I instantly recognized that making a puzzle where the song's title was revealed as one solved it would make it too tempting and too easy to fill in the blanks before finishing the puzzle. When I realized that I could use an AllMusic URL instead, I set off to figure out how to make a puzzle leading to that URL. The rest is history. :)

The randomly selected winners are ralphmerridew, Robert Vollmert, LordKinbote, and Jangler! Congratulations to you all!

On a completely unrelated note, look who else wished me a happy birthday!

Monday Mutant 79: Streampunk (all 3's)

Shade in some cells black such that the black cells are all connected to each other through their edges, and no 2x2 cell area within the grid contains all black cells. Numbers in a cell indicate the sizes of the orthogonally contiguous groups formed by black cells sharing a corner or an edge with that cell. For example, "3" means that the cell shares a corner or an edge with three black cells, and they form a single group, whereas "1 3" means the cell shares a corner with four black cells which form a group of three cells and a single separate cell. Cells with numbers cannot be black. A 3 or a clue with a 3 in it has been placed in every white cell that could legally contain one.

Monday Mutant 78: Streampunk

Shade in some cells black such that the black cells are all connected to each other through their edges, and no 2x2 cell area within the grid contains all black cells. Numbers in a cell indicate the sizes of the orthogonally contiguous groups formed by black cells sharing a corner or an edge with that cell. For example, "3" means that the cell shares a corner or an edge with three black cells, and they form a single group, whereas "1 2" means the cell shares a corner with three black cells which form a group of two cells and a single separate cell. Cells with numbers cannot be black.

Before you complain about me featuring a "classic" puzzle type (a modern classic, mind you, but a classic nonetheless), I quote a post of yore: Monday Mutants is a series in which I will attempt to experiment with "mutant" puzzles. These could be existing puzzle types with an unusual change in the rules, hybrids combining elements from multiple puzzle types, or puzzle types neither invented nor popularized by Nikoli. Also remember that in the weeks after that post, I played around with several variants on said "classic" puzzle.
Two of my Cross the Streams puzzles have been published in Akil Oyunlari! I encourage you to get a copy of the magazine so you can see them. Don't let the Turkish language daunt you; the magazine's LiveJournal is devoted to making the puzzles as navigable as possible for English speakers. :)

Monday Mutant 77: Proof of Quilt / Battleships

Ten ships (as indicated below the grid: one four-cell ship, two three-cell ships, three two-cell ships, and four one-cell ships) are hidden in the grid. The ships may be rotated from the orientations shown (without changing the numbers), but may not overlap or occupy cells which share a corner or an edge. A number to the right of a row or below a column indicates how many cells in that row or column are occupied by ships. These ships also function as black cells in a Proof of Quilt puzzle, and the numbers on some of the ship segments function as they normally would in such a puzzle. None of the black cells already present in the grid are part of the ships. Locate the ships and solve the Proof of Quilt puzzle.

This could be my strangest Monday Mutant in a long time.

Grant's Review Corner: Volume 6

At approximately 3:00 AM local time on May 2, 2011, I received this e-mail:

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.

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!

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!

Puzzle 493: Streaming Content 35

No comment.

Rules of Streaming Content

Monday Mutant 76: Battleships (minesweeper)

Ten ships (as indicated below the grid: one four-cell ship, two three-cell ships, three two-cell ships, and four one-cell ships) are hidden in the grid. The ships may be rotated from the orientations shown, but may not overlap or occupy cells which share a corner or an edge. A number in a cell indicates how many of the cells sharing a corner or an edge with that cell are occupied by ships. Cells with numbers cannot contain ships. Find the ships.

Combining Minesweeper and Battleships is probably one of the most ironic things that's ever happened in the realm of puzzles, since in Minesweeper, you want to avoid hitting mines, but in Battleships, you want to hit the ships.