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Puzzlesmith 1: Polyominous - The Zotmeister

solving the puzzle of life one entry at a time

Jun. 23rd, 2005

02:39 pm - Puzzlesmith 1: Polyominous

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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 ztm@cox.net, 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
        448832
        748836
        778866
        777666
        755550

     4) 418832
        448832
        748836
        778866
        777666
        755555

     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