Solution to Perfect Square 

Solution to Perfect Triangle

Special Note:  This puzzle is dedicated to the memory of "Bob" Martin, who passed away peacefully at the age of 71 a couple of days before Christmas, 2013.

The motivation for these two puzzles was to mark the 36th birthday of my assistant Christie Martin, which meant that both her first and last names needed to be in a suitable grid. I realized that 36 = 6x6, a "perfect square" (draw your own conclusions), and had the outrageous idea to create a puzzle of those dimensions with no black squares.  Of course, that meant that to fit in Christie's last name, a rebus would have to be used, and I thought the best chances came with the rebus word "TIE" (see pictorial hint, inspired by Phil Platt). The goal was to have as many recognizable words as possible, and to overclue them so as to give the solver every possible opportunity to complete the puzzle

So how did we do?  Our vaunted beta testers aced the Civil War battleground (11-Across), and the much-in-the-news governor of New Jersey (3-Down) [and this puzzle was written well before "Bridgegate"!], each of whom had been clued in ways that drew the rebus to the forefront. Christie's last name (3-Across) provided a shout-out to (the first name of) our good friends beta tester-extraordinaire Martin Herbach and legendary constructor Martin Ashwood-Smith. Giving equal time to an in-the-news politician from the other party, most solvers should have little trouble with 3-Across, while 4-Down is an interesting word harking back to times when many fibers (strings) came from natural rather than synthetic (polymer) sources. 5-Across is the plural of a term one occasionally encounters (fully spelled out as "boatswain") when reading seafaring fare; contracted, the spelling may give pause, but both the plural and (especially) singular are well-precedented in the Shortz-era databases.

But then it got dicey. I cringed at using the uncommon (Var.) spelling (1-Across) of what I had learned as sukkah [transliteration generally recognizes k's rather than c's, as per this puzzle]. 2-Down is a word beknownst only to the prolific Paula Gamache's wordlist, as well as the eclectic tastes (literally as well as figuratively) of the aforementioned Martin Herbach. 5-Down is a particularly obscure reference to an otherwise well-known character in a rather well-known Shakespearean play [this I know because my daughter Deborah played Celia in a "Shakespeare in the Parkview" production back when she was 11 years old, and her 13-year old brother Michael was one of the villains in the same production]. 1-Down is absent from all the crossword databases that I checked, but the hope is that pasting the clue into Google might scare up the answer. But then come the dreaded 9-Across intersecting 6-Down, which beta tester Ralph Bunker called "the single worst crossing [he] had ever encountered."  After considering, but rejecting an effort to tie 6-Down to a much more recognizable word (minus the bigram DO), I fell back on the anagram "trick" (though some would call it "act of desperation") to try to make that crossing just a bit more palatable. 

In the middle of all these conniptions, my friend Noam Elkies suggested a possible way out.  He pointed out that 36, in addition to being a perfect square, is also a triangular number = 1+2+3+4+5+6+7+8, and that even Methuselah never had another square-triangular birthday past 36.  [There is an infinity of numbers that are simultaneously square and triangular , but the list is sparse, starting 1, 36, 1225, 41616, 1413721, ...]  Noam further proposed that with the 6-letter (MARTIN) and 8-letter entry (CHRISTIE) locked, it might nonetheless be easier to fill an appropriate grid. [Technical note, the standard crossword compiler software is not really helpful for this, but with some ingenuity and good on-line word lists, this can be done manually while trapped in a seminar that doesn't require the full array of brain cells to take home its take-home message. Compare to Noam's It's a Trapezoid, although for our purposes, we elected to fill an isosceles right triangle, with 1-Across being a single-letter word, the remaining Across clue numbers being even numbers from 2 to 14, and the Down clue numbers along the hypotenuse being odd numbers from 1 to 15.]

In terms of the Perfect Triangle puzzle, I do not believe that there is much eyebrow-raising content in either the fill or the clues, especially since we did not need to rely on a rebus. The fact that our honoree's first name was clued with respect to two recognizable last names, those of all-time best-selling mystery novelist Agatha or legendary actress Julie, and that her last name was clued with respect to the shared first name of two recognizable actors (click here and here), may strike some solvers as mildly amusing.  As a chemist but also a Stuyvesant High School alumnus (as is Noam!), I plead guilty to cluing 2-Across for the sitting Attorney General, rather than for element 47 in the Periodic Table or for the colloquial way to refer to that branch of a college or University devoted to farm and veterinary studies.   Having been born in Hungary, I was pleased to enter 3-Down, and there is also a culinary flavor to 1-Down and 9-Down. As to the less-than-optimal 12-Across, click here (3-min video) for the actual song by someone whose last name comes up often enough in crossword puzzles [close race with first name of an Indy 500 car racer; pere not fils], and as to the pitiful 7-Down, hopefully this image will convince you.

Noam Elkies found a different triangle that met our constraints, and we are certain that interested readers may be able to develop yet others.

By the way, returning to the originally proposed Perfect Square, I've been having some fun exchanging e-mails and Facebook posts with new friend Evan Birnholz as to what the "worst puzzle ever" is. His nominations are this (3x3) and this (4x4), and we should not forget Peter Gordon's widely known version. Also, subsequent to the completion of the present puzzles, Michael Hanko and I constructed the ambitious A Tribute to N.C. Wyeth: The 40th Worst Crossword in the Universe.  Try it and tell us if you agree!

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