The Zotmeister

solving the puzzle of life one entry at a time

Mar. 23rd, 2012

01:23 pm - Puzzles 55-8: Polyominous

First off, a reminder (or introduction if you missed it earlier): I'm running a contest right here on my journal right now that technically isn't a puzzle but is very puzzle-like in nature; it's called "Oxendo", and you can check it out with that very link.

Grant Fikes - aliases include "mathgrant", "foxger", and "President of the Zotmeister Fan Club" - some time back in 2008 got sick of waiting for me to make another Puzzlesmith contest (es having missed my first - and so far only - one back in 2005) and decided to open es own reader-submitted puzzle gallery. Since then, four more "Logicsmith Exhibition"s have graced es weblog, and in a surprisingly non-ironic manner, I have managed to miss all but one of those myself... but what is ironic about it is that I kept asking em over and over to do more of them. Especially given that four of them were for Polyominous puzzles - something I consider a specialty of mine (I'd also note that Grant just up and stole my name for them!), I have long thought this a serious problem. Although I still plan on some more Puzzlesmith contests of my own - and eventually getting around to remaking the images for the first one! - I figured I'd take care of this chunk of unfinished business first, and in style: behold, my first puzzle tetraptych!

See Puzzle 7 for instructions.

Puzzle 55

Grant's first Exhibition had a lovely required givens pattern for a ten-by-eighteen grid. Even with only two entries to the original Exhibition - one of which was Grant's emself - I still was surprised no one else did what I did with the grid, something that came to mind pretty much immediately. I'm sure you'll know what I mean when you get to it.

Puzzle 56

This is the one I actually managed to not miss. Grant offered up a smaller grid with a denser required givens pattern in the hopes of pulling in more submissions, and it worked. The astute may notice that my '5's here look different. That's because this image is based off of the one I originally sent to Grant, which is before I started generally using the larger digits, much less finalized my "bigalpha" font. I figured I'd leave it that way for historical purposes.

Puzzle 57

The required givens pattern for es third gallery was so cluster-friendly that I figured I had to do something fairly technical in order to make the resulting puzzle actually interesting. As is hopefully immediately apparent, I'd like to think I succeeded. With apologies to Thomas Snyder, a mindgame: try to guess before you start solving whether any implied polyominoes will require a digit other than '1' or '4' :)

Puzzle 58

Grant's fourth Exhibition is for a different puzzle type - a weird one I have no experience with - and I have no real interest in that at this time. However, es fifth and most recent gallery is arguably even weirder - instead of a givens pattern, the requirement was quantity-based: exactly four of each digit from '1' to '9' (in any rotationally-symmetric pattern). In the write-up, e seemed quite willing to dole out accolades for those squeezing in two-digit implied polyominoes; I have to admit to making this in response, although what exactly I'm trying to say with it I'll leave as an exercise for those who really ought to be doing something else with themselves.

Right, so now that that's done... Logicsmith Exhibition 6, please! - ZM

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Current Music: "Peg", Steely Dan
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Jun. 14th, 2007

05:32 pm - Puzzle 47: Polyominous

See Puzzle 7 for instructions. This was the first puzzle I created in a new graph-paper notebook I acquired specifically for puzzle construction. I rather like this puzzle; it's fairly pretty, and has an interesting solving theme. Comments, questions, and emailed solutions are welcome as always. If you submit a solution, tell me what your favorite number is. - ZM

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Current Music: "The Voice", The Moody Blues
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May. 26th, 2006

06:39 pm - Puzzle 31: Polyominous

See Puzzle 7 for instructions.

So [ profile] glmathgrant emails me and says:

I know this is short notice, and you have a bunch of video games and stuff to concentrate on right now, but if you could make a puzzle and post it on your blog on May 26, it would feel really special. I don't care what kind of puzzle it is. It can even be really easy, like a 2x2 Sudoku puzzle, or a Hashiwokakero puzzle with just two islands, or a Slither Link puzzle with the number 4 in it! (Ridiculously easy puzzles are so underrated; I'm glad Puzzle Japan has an archive of its April Fool's pranks where some "ultra hard" puzzles would be posted on the site, because some of those easy puzzles are sheer artistry!)

Now I may not be a rich man, but I am a man of many treasures, and I do so much enjoy being able to give people exactly what they ask for.

Happy birthday. - ZM

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Dec. 21st, 2005

02:17 pm - Puzzle 23: Polyominous

See Puzzle 7 for instructions; the colors are purely aesthetic, to keep my "clock" design from being lost amongst the other givens. I don't know the significance of 5:07 any more than I know the significance of the $5.07 donation to my PayPal account. A Polyominous was requested, so that's what I made; I had to do something to celebrate this first reimbursement, but that peculiar amount was my only muse. I hope you all enjoy this as much as I'll enjoy the Nikoli book that that money will inevitably purchase. As always, email me your answer if you want it checked, and I might have something extra for you. - ZM

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Aug. 30th, 2005

03:23 pm - Puzzle 15: Polyominous

See Puzzle 7 for instructions. Phew - this was exhausting to build! Yes, your eyes do not deceive you - those are twenty-ones in the corners. Also be on the lookout for... oh, but that would be a spoiler. I'll just let you try to find it yourself. Email me when you solve it, and if you haven't found it by then, I'll point it out to you. Of course, any generic comment about the puzzle is welcome to be posted right here. - ZM

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Jul. 24th, 2005

11:39 am - Puzzlesmith 1 Results

I am pleased to report that I had only one fewer entry than I expected to receive. Both were perfectly valid, with a unique solution and rotationally symmetric givens. It turns out that with my own "entry" included, all three of us each used only eight givens. I'd imagine six would be impossible, but I certainly haven't proven this. All three puzzles are duplicated below - enjoy (see Puzzle 7 for instructions):

I thought it interesting to note the variances in our compositions. Cameron pulled off what I was aiming for at first and failed to do with only eight givens: no givens on the outer border; Jezendar has a parity apartheid thing going, with the even-celled polyominoes separated from the odd-celled (which e claims e didn't notice until after e built it); my givens are all different values.

With the assistance of, Jezendar has been selected to receive the fifty-dollar prize. Congratulations! You should be getting an email from PayPal shortly.

Shameless plug: there's another way to get a hundred dollars out of me open right now. If that isn't your proverbial cup of tea, fear not - I'm already planning more puzzle contests. - ZM

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Jun. 23rd, 2005

02:39 pm - Puzzlesmith 1: Polyominous

It occurred to me recently that I've been making puzzles for my readers, but no one has been returning the favor... so here is a open solicitation for puzzles thinly disguised as a contest.

[Note to any LiveJournal lawyers: This is not an advertisement - this contest has no corporate sponsor. The prize is to be paid out of my personal pocket; Paypal will serve only as the conductor of the transaction, and will be used solely due to convenience and privacy maintenance. As far as I can tell, this contest does not violate the Terms of Service. If I am wrong, I will gladly amend whatever I need to; my email address is on my User Info page.]

My fascination with puzzles runs deep into their mechanics. I have so far published two Polyominous puzzles; I'd like to see how others can do, and test a theory I have. I'm challenging you to build a puzzle to my specifications, and to do so as efficiently as possible.

The challenge is to create a Polyominous puzzle with a six-by-six grid such that its solution contains one polyomino of each size from 1 to 8 exactly once. Of the thirty-six cells of the grid, one will be a monomino, two will make a domino, and so on up to eight making an octomino (8-omino). Note that the integers from 1 to 8 inclusive sum to 36, so this comes out even.

It's trickier than it may seem, since a large part of building a Polyominous puzzle typically involves taking advantage of the rule preventing same-sized polyominoes from being adjacent. Here, every polyomino in the solution must be a different size, so this is not so readily applied.

The puzzle you build must be a standard Polyominous puzzle - it must have exactly one solution following the standard rules. You may NOT assume that a solver knows in advance of viewing the grid that all of the polyominoes in the answer are unique in size. In addition, the givens - the numbers you place in the grid for the solver to work with - must appear in rotationally symmetric cells, like the black squares in most crossword puzzles. For example, if you place a number in the second cell from the left on the top row, you must also place a number in the second cell from the right on the bottom row (which would be second from the left on the top row if turned upside-down). As a result of that and the grid size, you must have a even number of givens.

The objective is to create this puzzle with the fewest givens possible. I believe I know the answer, but I may well be proven wrong.

I dug up the last of my old Sanctum Puzzlers for reference in crafting these contest instructions:

This contest is open to anyone eighteen years of age or older with a Paypal account, apart from myself.

Email the following information to, with the subject line Puzzlesmith 1 Entry (do NOT edit the subject line!) when you think you have your best solution:

1) Your name or nickname (whatever you wished to be credited as);
2) The number of givens your puzzle employs;
3) The puzzle grid itself, typed cell by cell, one row per line, with zeroes used for blank cells;
4) The solution grid, typed cell by cell (numbers only), one row per line;
5) The email address you would like your prize sent to (if different from the one you sent your entry from).

Here is an example of a perfectly valid entry:
     1) TwoDigitIQ

     2) 34

     3) 018832

     4) 418832

     5) l33t@Pwnz0r.joo

I certainly hope you can make a better puzzle than that.

Any questions may be posted here as comments, and will be answered if fair (of a clarifying nature, as opposed to giving hints).

All entries must be received on or before July 23, 2005, Eastern Daylight Time.

Limit one entry per person. Duplicate entries - including one person sending multiple entries via more than one email address - can result in their submitter being banned from this and future contests.

Entries can NOT be edited after submission. Requests to edit entries will be construed as duplicate entries (see above). So be certain you've done your best before you enter; I am NOT responsible for any injury you inflict upon yourself if you find a better answer after you hit Send on your mail program.

By entering this contest, you grant me the right to publicly display any or all of your entry apart from email addresses after the contest due date; entries will be kept strictly confidential until then.

The top entrant will receive $50US via Paypal. Ties will be broken by random draw. I will double this prize, to $100US, if the solution of the top entrant uses strictly fewer givens than my own solution. No, I'm not telling you how many it took me. I am the sole judge of whether or not the prize will be doubled. It may not even be possible to double it, but I've learned in the past that I can be very surprised by the entries to contests such as this.

I maintain the right to cancel this contest at any time without awarding any prize, but intend only to exercise such right in the event of unforseen circumstances.

That's all - get cracking! - ZM

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May. 12th, 2005

03:38 pm - Puzzle 9: Polyominous

Not even waiting for my last puzzle to be solved...

See Puzzle 7 for instructions. For the record, I make these puzzles to challenge myself: the trickier the logic I use to successfully construct a puzzle with a unique solution, the more I've mastered the design. This makes for harder puzzles; I'd like to think this makes them more rewarding to solve. I bring this up because this may be the hardest puzzle I've yet built for this journal. Your comments are welcome, and of course, emailing me your solution may be more rewarding than just the satisfaction.

Incidentally, I have several puzzles already constructed that I simply haven't pixelized and posted here, but I'll get around to them eventually. In the meantime, does anyone have any requests? Let me know what you'd like to see more of; if there's a puzzle type I haven't posted here that you're fond of, tell me about it (or better yet, point me to a website featuring it), and perhaps I can build some for you. Donations to my PayPal account may prioritize your request♪ - it would be nice to have a stash for providing prizes♥ (I've actually given away close to a hundred dollars worth already - you never know what I'll offer if you send in your answer.)

Enough ado - here's the puzzle. - ZM

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Apr. 22nd, 2005

04:03 pm - Puzzle 7: Polyominous

The pun is so obvious, I'm surprised no one else has used it as a name for this puzzle. But then again, maybe that's exactly why they haven't.

A polyomino is a tile made of a group of squares. The video game Tetris gets its name from the pieces being tetrominoes - that is, four-unit polyominoes. A two-unit polyomino is called a domino, a term most should be familiar with; a one-unit polyomino is called a monomino. For those who want to hum along without learning the words, a polyomino of n units can be called an n-omino, so a tetromino can be called a 4-omino, a polyomino with fourteen cells is a 14-omino, and so on.

On the left is an unsolved Polyominous puzzle. On the right is what its unique solution would look like if solved with purple ink.

The object is to take the given grid and divide it into polyominoes such that each given number n in the grid is part of an n-omino and that no two polyominoes of matching size (quantity of cells) are orthogonally adjacent.

Yes, that's the entirety of the rules in one sentence. It's a simple puzzle. But for the checklist lovers out there:

1) Except for the outside border, the puzzle grid shows only the corners of the cells of the grid. To solve the puzzle, draw in the needed borders between cells so as to divide the grid up into sections following the remaining rules.
2) The number of squares in each section created by the borders must match the number in any cells of that section. (So if there's a 2 in the grid, the section with that 2 must have exactly one other cell with it, making two cells total.)
3) Two sections with the same number of cells cannot be orthogonally adjacent - that is, they may not touch except at corners. It is strongly recommended that as you learn what cells belong to what sections, you write in numbers in the blank cells - just like those already in the grid - so that you don't violate this rule. (So if you have a three-cell section, you can't have another three-cell section sharing a cell side with it. If you write a '3' into each cell of the section that needs it, you'll know not to write another '3' next to it as part of another section.)

Note that this isn't Islands in the Stream. The numbers in the grid are not necessarily one-to-a-polyomino. You can have multiple given numbers in the same section, like the triomino (3-omino) in the upper right of the sample, or even no digits at all, like the monomino in the upper left of the sample. You'll need to pay careful attention as you're divvying up the grid. Don't settle for trial and error - stick to logical deduction.

How to solve the sample puzzle )

This was an interesting one to put together. I had some fun with patterns in the given numbers. It starts out easy enough, but I recommend caution as it goes along. Comments are welcome as always, and emailing me your solution might get you something. Note that a simple grid of numbers, if you fill in all the blanks, is sufficient to express the answer; the borders are trivially deducible from that. - ZM

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