GAME OVER: BETAVEROS WINS!
Please view the comments for the solution, &c. (I'm leaving the main entry text spoiler-free for posterity).
Valid koans are 4×4 grids of letters in the word 'OXEN'.
These grids have the Buddha-nature:
NOXE NEOX EXON NNNN NNNN NNNN NNNN NNNN
EXON ENXO NOXE NNNN NONN NONN NNON NOXN
ONEX XOEN XENO NNNN NNON NNNN NOON NENN
XENO OXNE ONEX NNNN NNNN NNNN NNNN NNNN
ONNO XNNX NXNN ENXO ONOX NNNN ONOO OXEN
NNNN NNNN NNXN XOEN XONO NXXN OXXN ONON
NNNN NNNN XNNN OXNE NOXO NXXN NXXO XNXN
ONNO XNNX NNNX NEOX OXON NNNN OONO XNXO
These grids do not have the Buddha-nature:
OXEN OXEN OXEN OOOO OXOX OXEN OXEN XXXX
ENOX ENOX NEXO XXXX XOXO XONE XENO EOXN
OEXN XENO XONE EEEE NENE ENOX ENOX EXON
EONX NOXE ENOX NNNN ENEN NEXO NOXE XXXX
ONEX OOOO ENEN XXXX EEEE NONO OOXN OXEN
NOXE OOOO NONO XXXX EEEE NONO OXEN XENE
EXON OOOO OXOX XXXX EEEE NONO XEEN ENEX
XENO OOOO XEXE XXXX EEEE NONO NNNN NEXO
EEEE NNNN OXEO NOEX ONOO OOOO NNNN NNNN
ENEE OOON XNNE ONXE OXXO ONNO NOON NOON
EENE OOON ENNO EXNO NXXO ONNO NOON NOON
EEEE NOON OEXO XOEN OOON OOOO NOON NNON
The Buddha-nature is animal related.
All suppositional koans and guesses at the Buddha-nature must be presented here as comments - emails, private messages, &c. will not be considered. One koan per person per sweep limit, with "sweep" defined as when I get around to updating this entry with everyone's koans. (This should be roughly daily.) If you guess at the Buddha-nature [there is no prerequisite for this - there is no Mondo nor are there guessing stones here], you may not present a koan in the same sweep, and if the guess is incorrect you may not present koans nor guesses until two more sweeps have been performed. If the guess is correct (and you're the first to do so), well, then you win... something. I haven't decided yet. This whole affair is intended to be fun and informal.
And in case you're wondering, yes, Grant Fikes was again indirectly responsible for this. I got the idea for this at MIT before the Hunt started when I saw devjoe piecing together an image for a "pixel Zendo" game mathgrant was running somewhere. It was the first I'd heard of Zendo, actually. I just figured I'd put this out here and see what happens. - ZM
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 random.org, 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
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 firstname.lastname@example.org, 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:
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