“Digimix”

Whew. I just now finished this week’s Listener puzzle, called “Digimix” by Oyler. A number puzzle this week, and a very tough one. In order to fill the grid, you have to deduce eleven pairs of numbers, one of four digits and one of five, which have the properties that (a) they contain between them the nine digits from 1 to 9, once each, and (b) the sum of their squares is a nine-digit number that likewise contains the nine digits from 1 to 9, once each. This nine-digit number is broken into three three-digit numbers, so that each set contains five numbers (a four-digit, a five-digit, and three three-digit). The sets then contain 55 numbers in all, and most of these are clued in terms of grid entries. For example, one of the three-digit numbers is clued as b + e + p, and b, e, and p are entries in the grid (which is like a crossword grid but lettered rather than numbered).

It took me about five minutes on Friday afternoon to break into the grid, as the constructor kindly put an obvious clue in the first set of numbers — one of the three-digit numbers is a multiple of another, so between them they must contain six different digits, none of them zero. Other factors limited the values of the two numbers, and it wasn’t hard to run through the possibilities and find the only one that worked. That quickly gave me six squares filled in the grid.

I am giving next to nothing away by saying that much. It took only five minutes to get those, and then by Friday evening, despite a few pages filled with scribbled calculations that didn’t lead very far (for example, I had deduced that the last digit of a certain grid entry could only be 2, 5, or 8, but I could see any way to use this information to get any further), I still had only those six squares filled. By Saturday afternoon, I had a grand total of eleven. (The grid is nine squares by seven squares, or sixty-three in all.) But on Sunday I spotted a couple of deductions I could make that I had overlooked before, and those put useful limits on what some of the numbers in the sets could be.

I ended up getting out the laptop and doing some of the calculations in a spreadsheet program, and that made things much easier; this would be a much more tedious puzzle to solve with just a calculator. Several times I found that I’d narrowed the possible combinations of a few numbers down to six, or twenty-four, or in one case sixty possibilities, and what I needed to do was run the same series of calculations on all of them and see which ones led to possible answers. Much easier to do this in a spreadsheet, where I could set up the series of calculations just once and then quickly apply it to all the possibilities.

It feels a bit inelegant to me somehow that the puzzle needed this kind of brute-force approach (unless I’m just missing the way to solve it without it); but then, at the same time I can’t actually see a rational reason why a spreadsheet program should seem too much to me while a calculator and a printed table of square numbers seem perfectly acceptable tools to me (which they do); they’re all just timesavers for calculations I’m perfectly capable of making with pen and paper alone but don’t want to because it would be long and dull.

But the puzzle certainly wasn’t all about brute force with a spreadsheet. There were a lot of surprising and tricky deductions I had to make along the way, and it was very satisfying to figure those out.

(For those who find this entry because they’re actually trying to solve the puzzle: Yeah, I found the preamble confusing, too, and I think it’s poorly worded. Try changing the first three words to In each of the eleven horizontal rows of clues below. I was confused by the boldface letters at first, too; they aren’t clues themselves, they’re headings for the vertical columns of clues below them. Capital letters in the clues stand for across entries in the grid and lowercase letters stand for down entries. In the final sentence, I am assuming that missing entries should be missing clues because nothing else seems to make sense; all the entries are missing, obviously, because the grid is blank when you start.)

First Draft of Scene Four Done

Finished the first draft of scene four over lunch. This scene was great fun to work out — the situation contains both a lot of tension and a lot of humor. The first act as a whole (which will be eight scenes in all) ought to feel like a roller coaster ride for the central character, or like a tale out of the Thousand Nights and a Night, with unexpected developments and reversals at every turn. I think that’s how it’s coming out.

There’s a small incident I wanted to work into this scene, though, that I couldn’t — the main character, who can’t read or write, asks somebody to write down a few lines he’d heard and which have some emotional significance for him, so that he won’t forget them and lose them forever. I had worked out in outline how it would fit in with the other events in this scene, but when I got into the actual writing, I found that it didn’t work; from the beginning of the scene the main character is in too much of a life-or-death situation for it to make good sense for him to stop for this matter.

It’s a small moment but it ties into two other moments in other scenes, and if I can’t shoehorn it somehow into scene five, it’ll be too late for it to happen and I’ll have to cut the other two moments as well.

Good Writing Day

Good writing day yesterday. After lunch with Dave and friends, I helped out at the bookstore for a little bit, changing an outlet in the upstairs office to three-prong and putting some curtains over the windows to keep the room cooler. Then over to Sweet Adeline with my laptop and books, where I worked on scene four for a couple of hours. I got four or five pages written — probably about two-thirds of what the length of the scene will be — and I think it’s very good stuff, too.

When I write something meant to be spoken or sung out loud, lyrics or dialogue, I read it out loud as I go. I write the line, and then I imagine myself as the character in the situation and I say the line and see if it feels right for the character to say it. And I also imagine myself in the audience and I try to feel how I’d react to the line if I were hearing it for the first time, and see if it creates in me the reaction I would like it to create in the audience. Usually, of course, there’s something wrong with the line and I have to make an adjustment and try again, and sometimes it takes many, many tries. So there I am in Sweet Adeline, typing away and saying everything I’m typing under my breath, and I can only imagine that anyone taking notice of me was thinking, oh that poor man, he can’t type without moving his lips.

I want to get a good first draft done of the first act (of three) as soon as I can. I think there will be eight scenes in the act, so I’m about halfway there. And it feels very good to be moving forward with it again.

“Double Shuffling and Dealing”

I found this week’s Listener puzzle particularly difficult. I started Friday afternoon, and although it was competing for my attention with a few other things, I must have given it a good hour or more before going to bed that night, by which time I had solved exactly one clue. By lunch the next day I had solved two more.

Still, I chipped away at it, and by the end of the day Sunday I had the upper left corner of the grid filled in. Each answer contributes one letter to a Shakespearean quotation, and I had enough letters at this point to make a good guess at two consecutive words of the quote, at which point I was able to find it easily (doesn’t everyone have a Shakespeare concordance on their cell phone?). The quote then gave me a general idea as to what was going on with some of the clues that hadn’t been making sense.

This morning I finished the puzzle on the way to work, except that I haven’t rearranged 15 letters to form a second quotation. But you don’t need that to finish the grid, you only need to find and highlight in the grid the name of the second playwright, and I’ve done that. So I’m really to submit my entry whether or not I figure out the phrase.

Very Warm for May at 42nd Street Moon

Dave and I went to see a small production of Hammerstein and Kern’sVery Warm for May at 42nd Street Moon last night. I’d always read that this was one of both men’s favorites among their musicals and that they were both very disappointed in its failure on Broadway, so I was all prepared for something no doubt flawed in its construction or uneven in its writing but with plenty of charming and special qualities all the same. At the end of the first act, though, Dave and I looked at each other with dismay — this dog of a show was the one they remembered fondly? The story and characters seemed both trite and clumsily written, the songs made very little impression, and the moments of real charm and wit were few. However, the second act started out a bit better, and continued getting better and stronger as it went along, and by the end of the show I could see how you could feel some affection for it.

Very Warm for May has a rather loose story about a theatrical family and an amateur production of a new musical, and probably works best as a vehicle for a bunch of talented and characterful performers. It doesn’t get that here; only Bill Fahrner as the eccentric writer and director of a very strange musical and Maureen McVerry as the wealthy woman who owns the barn in which the musical is being rehearsed created distinctive characters for themselves and had the presence and comic timing to make their roles sparkle. None of the others was bad or anything, they just didn’t seem very sharp. (Jimmy Robertson was only so-so in the spoken portions as the director’s geeky assistant, but suddenly outshone everybody else whenever dancing started.) That and a tendency to keep the musical numbers at an unvaryingly brisk pace gave the production a bit of a mechanical feeling sometimes.

One thing I found very interesting about the show was seeing how Hammerstein reused ideas from Very Warm for May in later shows. Dave and I had just been talking a couple of weeks ago about how playwrights and composers often recycle things from their failed or forgotten or unfinished works, and here you could see where Hammerstein had done the same; Very Warm for May contains early versions of ideas that later became “Song of the King” from The King and I, “Sixteen Going on Seventeen” from The Sound of Music (though I might argue that A.E. Housman got to that one even earlier), and especially a whole lot of Me and Juliet.

Dave also speculated that Hammerstein may have gotten more than a few ideas for Very Warm for May out of Die Meistersinger, a suggestion that seems ludicrous until you actually stop and work it out.

I’m not 100% sure but I think one of the dances contained a rather snarky “quotation” from another well-known dance number from another show. I really dislike that sort of thing when it pulls me out of whatever involvement I was feeling with the characters and the story at that point. I laughed when I recognized the steps (or thought I recognized them), but if I’m right about the “quote”, it was kind of a cheap shot that didn’t have anything to do with the situation in the story, and I felt a bit slimy afterward for having laughed.