Tuesday, May 1, 2018

Another Note On The Even/Odd Puzzle

It's an interesting question how many numbers are consistent with a given list of letters, such as this list of letters from our Even/Odd puzzle:

a, b, d, f, f, h, h, i, i, i, i, i, i, l, l, l, l, m, n, n, n, o, o, o, o, o, o, r, r, r, s, s, t, t, t, t, t, u, u, w, x, y, y

Suppose we determine the words that gave rise to the list:

two, four, six, thirty, forty, thousand, million, billion.

Then we can ask, which number words can be assembled from these words (adding hyphens where necessary)? The answer will have to fit a frame like so:

_____ billion, _____ million, _____ thousand, _____.

Note that the fourth blank could be empty, as happens for example in forty-six billion, thirty-four million, two thousand.

To determine how many ways there are of filling in the frame, I picked up a pen and systematically listed 24 possibilities by hand—all the cases in which no blank is left empty and in which the decade words (thirty, forty) appear in the last two blanks. Now the decade words could also go in the first two blanks, or the first and third, or the first and fourth, or the second and third, or the second and fourth; considering those additional five groups of possibilities, there are 24 + 5 × 24 = 144 possibilities, assuming the final blank gets a word.

It remains to count the possibilities in which the final blank remains empty. There are three ways to choose the two blanks where thirty and forty will go. Having chosen those two blanks, there are two ways to place the two decade words. Having placed the words, there are three ways to choose which single-digit word doesn't get paired to thirty and forty with a hyphen. And finally, having made that choice, there are two ways to match the two remaining single-digit words with thirty and forty. So altogether there are 3 × 2 × 3 × 2 = 36 possibilities in which the final blank remains empty.

Together this is 144 + 36 = 180 possible numbers that, when alphabetized, match the list of letters given in the original puzzle.

I didn't try to list all the possibilities by hand, but I wrote a computer program to list them. The logic of the program differs from the counting analysis sketched above. The output was the 180 numbers shown below, all of which yield an alphabetized list of letters identical to the one given in the original puzzle.

Update 5/16/2018: Reader Sue pointed out that I neglected to say which number generated the original puzzle! Sorry! It was 4,036,002,040 (indicated below by an asterisk).


2,004,030,046
2,004,036,040
2,004,040,036
2,004,046,030
2,006,030,044
2,006,034,040
2,006,040,034
2,006,044,030
2,030,004,046
2,030,006,044
2,030,044,006
2,030,046,004
2,034,006,040
2,034,040,006
2,034,046,000
2,036,004,040
2,036,040,004
2,036,044,000
2,040,004,036
2,040,006,034
2,040,034,006
2,040,036,004
2,044,006,030
2,044,030,006
2,044,036,000
2,046,004,030
2,046,030,004
2,046,034,000
4,002,030,046
4,002,036,040
4,002,040,036
4,002,046,030
4,006,030,042
4,006,032,040
4,006,040,032
4,006,042,030
4,030,002,046
4,030,006,042
4,030,042,006
4,030,046,002
4,032,006,040
4,032,040,006
4,032,046,000
4,036,002,040*
4,036,040,002
4,036,042,000
4,040,002,036
4,040,006,032
4,040,032,006
4,040,036,002
4,042,006,030
4,042,030,006
4,042,036,000
4,046,002,030
4,046,030,002
4,046,032,000
6,002,030,044
6,002,034,040
6,002,040,034
6,002,044,030
6,004,030,042
6,004,032,040
6,004,040,032
6,004,042,030
6,030,002,044
6,030,004,042
6,030,042,004
6,030,044,002
6,032,004,040
6,032,040,004
6,032,044,000
6,034,002,040
6,034,040,002
6,034,042,000
6,040,002,034
6,040,004,032
6,040,032,004
6,040,034,002
6,042,004,030
6,042,030,004
6,042,034,000
6,044,002,030
6,044,030,002
6,044,032,000
30,002,004,046
30,002,006,044
30,002,044,006
30,002,046,004
30,004,002,046
30,004,006,042
30,004,042,006
30,004,046,002
30,006,002,044
30,006,004,042
30,006,042,004
30,006,044,002
30,042,004,006
30,042,006,004
30,044,002,006
30,044,006,002
30,046,002,004
30,046,004,002
32,004,006,040
32,004,040,006
32,004,046,000
32,006,004,040
32,006,040,004
32,006,044,000
32,040,004,006
32,040,006,004
32,044,006,000
32,046,004,000
34,002,006,040
34,002,040,006
34,002,046,000
34,006,002,040
34,006,040,002
34,006,042,000
34,040,002,006
34,040,006,002
34,042,006,000
34,046,002,000
36,002,004,040
36,002,040,004
36,002,044,000
36,004,002,040
36,004,040,002
36,004,042,000
36,040,002,004
36,040,004,002
36,042,004,000
36,044,002,000
40,002,004,036
40,002,006,034
40,002,034,006
40,002,036,004
40,004,002,036
40,004,006,032
40,004,032,006
40,004,036,002
40,006,002,034
40,006,004,032
40,006,032,004
40,006,034,002
40,032,004,006
40,032,006,004
40,034,002,006
40,034,006,002
40,036,002,004
40,036,004,002
42,004,006,030
42,004,030,006
42,004,036,000
42,006,004,030
42,006,030,004
42,006,034,000
42,030,004,006
42,030,006,004
42,034,006,000
42,036,004,000
44,002,006,030
44,002,030,006
44,002,036,000
44,006,002,030
44,006,030,002
44,006,032,000
44,030,002,006
44,030,006,002
44,032,006,000
44,036,002,000
46,002,004,030
46,002,030,004
46,002,034,000
46,004,002,030
46,004,030,002
46,004,032,000
46,030,002,004
46,030,004,002
46,032,004,000
46,034,002,000

Sunday, April 29, 2018

Solution to "Even Or Odd?"

I am thinking of a large whole number. If you write out the name of the number in English, and then alphabetize all the letters, you obtain the following result:

a, b, d, f, f, h, h, i, i, i, i, i, i, l, l, l, l, m, n, n, n, o, o, o, o, o, o, r, r, r, s, s, t, t, t, t, t, u, u, w, x, y, y

Question: Is my number even or odd?


Several readers submitted the correct answer, "even." Those who shared their method all found the answer the same way, namely by recognizing that every odd number has a name that contains at least one instance of the letter e. Because there's no e in my list of letters, my number must be even.

(I learned the fact about odd numbers recently on Buzzfeed, but now I can't find the listicle. Verifying the fact isn't hard once it's pointed out.)

Several readers went further and determined which words could be spelled using the given letters. For example, the presence of a b means that the number must include some billions, and the presence of an m means that the number must include some millions. Eventually one finds that the list arises from alphabetizing the following words:

two, four, six, thirty, forty, thousand, million, billion.

Many numbers can be spelled by assembling these words (using hyphens where necessary). I think the smallest and largest, respectively, are 2,004,030,046 and 46,034,002,000.

Thanks to all who submitted answers, arguments, and additional thoughts!


Thursday, April 26, 2018

A reflection about the end of my parents' life


When my parents entered long-term care, it wasn't natural for us to suddenly be physically affectionate with one another—but I adjusted my comfort zone anyway. A few hugs weren't going to kill us.

After my first wife left me, I flew from California to Detroit to visit my parents. I was twenty-three. When I told my dad what had happened, he replied that he'd been engaged once to a woman who broke it off, and that "today I wouldn't cross the street to say hello to her." Then, after placing his hand briefly on my shoulder, he wandered off. My dad and I never spoke again about my first marriage (what else was there to say?), and to the best of my recollection, his hand on my shoulder was the first time we had ever touched. That was how we were with one another, and it suited us both.

Decades later I decided that my father and I had underplayed this sort of thing, so when he lived in a nursing home I hugged him at the end of each visit. I believe he enjoyed this. (By then he'd been incapacitated by a neurodegenerative disorder and couldn't reciprocate or even react.)

My dad was a philosopher by nature, but for all her crackling brainpower the same couldn't be said of my mother. In her last couple of years, she faced decline with embarrassment and sadness. I hugged her then, or jogged her foot a little as we spoke, so as to press a silent argument. You might recoil at yourself, but I'm not going to recoil from you. It didn't make any difference, but then again, winning an argument with my mother was like trying to get a second sentence out of my dad. My parents and I took each other for what we were—loved each other for what we were. We might have enjoyed each other more if we'd taken more chances, earlier in life, to be a little different than we were.

Monday, April 23, 2018

Even or Odd?

I am thinking of a large whole number. If you write out the name of the number in English, and then alphabetize all the letters, you obtain the following result:

a, b, d, f, f, h, h, i, i, i, i, i, i, l, l, l, l, m, n, n, n, o, o, o, o, o, o, r, r, r, s, s, t, t, t, t, t, u, u, w, x, y, y

Question: Is my number even or odd?

Sunday, April 15, 2018

Book Review: Hood Struggle


Hood Struggle, by Kevin Guillard
A.R. Publications, LLC, 2013
Softcover, 255 pages
This review contains profanity in its quotations.




Antoine was pacing across the street from the bus station when he saw Blue Black coming up to him.
     "Say Toine, I got us a lick."
     "Where 'bout," Antoine asked.
     "They got this old white lady smoking a cigarette behind the bus station with her purse sitting on the ground. I know she got some money in that bitch."
     "She back there now?" Antoine asked.
     "Yea, but look; you can't just run back there and take it, because they got a camera sitting right over your head as soon as you go in that part. The camera is not facing your way. It's facing the back door. You gotta stand sideways with your back turned to the edge of the wall. Like this," Blue Black demonstrated how Antoine had to stand. "This way the camera could only see the back of ya head and not cha face. Ask her for a cigarette first, because the purse sitting behind her legs a lil' bit. When she get it and hand it to you, then you snatch it."
     "Aiight," Antoine replied. It never donned on Antoine why the hell Blue Black ain't do it his self.
     When Antoine approached the old lady, he seen that he really didn't have to ask for the cigarette, because the purse wasn't under her leg; it was on the side of it. He went ahead and asked anyway and made sure that he was standing the way that Blue Black had told him. After the old lady gave him the cigarette, he asked for a light. Antoine put the cigarette in his mouth and she gave him a light off the cigarette that she was smoking. When the tip of Antoine's cigarette touched hers, he couldn't help but notice how badly the woman's hand was shaking. That's when Antoine's senses kicked in.
     "Thank you, mam." Antoine said, then turned around and walked away.

In the poor Black neighborhoods of Baton Rouge, Louisiana, Antoine is growing up fast. At the beginning of the story, Antoine is living with his Aunt Monique and scamming the occasional crackhead by selling fake drugs. Antoine gradually becomes a seller in the real drug market, gaining ever more money and prestige as well as a girlfriend. He's a believable adolescent character grappling with innocence and experience within a vividly evoked culture. Sometimes Antoine's story is told in first-person narration, enhancing the character portrait. Several other characters are also given first-person soliloquies. Whatever the mode (soliloquy, dialogue, or internal monologue), the characters in the book speak realistically and with lively concision. Here's Monique giving us some of her story:
When I was younger, my momma was able to scam the Welfare office by getting them to believe I had a mental problem. Me personally, I don't think anything is mentally wrong with me, even though I have been known throughout the projects to fuck a bitch up at the drop of a dime.

The plot of Hood Struggle builds to a suspenseful climax, followed by a rapid denouement. The ending is satisfying not because it ties together the novel's many threads, but because it brings the novel's central concerns into sharper relief.

One of the best set-pieces in the book is when several characters hatch a plan to rob a high-rolling dice game. The heist requires a femme fatale on the inside. Apart from its rough prose and vocabulary, this subplot could be from Elmore Leonard. Here's how it begins:
=The Plot=
"Troy, tell me about that brod again," Lester asked.
     "Damn Lester, I been telling you for the past two days now. Clean out cha fucking ears." Troy said. "Look, the bitch said the nigga throw a dice game every night. Nothin' but big balling ass niggas be in there rocking platinum chains, Rolex's, and fifty-thousand dollars pinky rings and shit. It be 'bout fifteen niggas and each one of'em have at least seventy-five grand on'em."
     "Mane, how you know fa'sho you got the brod and that she ain't just playing games wit' chu?" Carl asked. The group of three stood in a small circle in Monique's back yard on a sunny day as the plot began.

Hood Struggle isn't all crime and danger. Monique is a significant character, and her story helps to flesh out the milieu. There are a number of funny situations, including some raunchy ones. Here's Antoine describing a video he watched during a sex-ed class at school one day:
"eeeeewwwwww," was the only thing that could be heard throughout the gym.
The shit made my eyes squinch. The nigga was fucked up. He had a green mole on his dick head with puss coming out of it. The next picture they showed made me regret that I even caught a glimpse of it. When I say the dude was tore up, that's not even the half of it. He had bumps, moles, warps, and a whole lot of other stuff all over his shit. The conclusion that I got from the glimpse was, kill ya'self.
After the video ends, "about eight hands automatically went up." The students in the class ask a number of questions about sexually transmitted diseases, and the teacher patiently answers them. The length of this exchange, and the factually dense answers from the teacher, made me think that Guillard was taking an opportunity to educate his young readers on an important topic. If so, then good for him. Part of the purpose of the book is social, as Guillard explains in some prefatory remarks:
The purpose of me writing this book was to see if I could open a few eyes in the urban neighborhoods. We're seeing it happen every time we turn our television to the 5:00 news channel or when we simply open the front doors and take a step outside. It's happening so close that it's now under the same roof as us. I think that I'll be fair and accurate to say that out of 95% of the families in the urban neighborhoods, there's at least one member that's been incarcerated before. Whether it's a brother, sister, uncle, or a parent. Some families have relatives that are never coming home again, and to those my heart goes out. To the families that have lost a love one by the hands of a gun, my deepest sympathies and my heart goes out.
My name is, Kevin Antoine Guillard, I'm 25 years old and currently incarcerated. …
The prison stay during which Hood Struggle was written ended some time ago, and Mr. Guillard has evidently put the last few years to good use, including by starting a company, A.R. Publications, to publish the manuscript.

According to the author's preface quoted above, Hood Struggle wasn't really written for me; that's why I've waited so long to review it. I didn't want to lightly join a conversation that I wasn't invited to, and I also didn't want to risk inappropriately applying tools of criticism to a work from outside the conventional literary enterprise. Despite all that, I'm reviewing Hood Struggle because to write a novel is to desire that it be read—a principle that applies as much to Kevin Guillard as to Rachel Cusk or the other writers whose books I've reviewed here.

I also don't want to overemphasize the book's stated purpose, or the author's life background, because to do so would slight the artistic value of Hood Struggle. We all know how tedious "message art" can be. Hood Struggle isn't a jeremiad, manifesto, or sermon; it's a page-turner with moments of suspense, sadness, and raunchy comedy. The book is rough-hewn, yet it has a subtle interior shape. Reading Hood Struggle was a thought-provoking journey to an environment remote from my own experience.

I had the pleasure of meeting Mr. Guillard in New Orleans last year when I was browsing in the French Market. He was seated behind a table stacked with copies of Hood Struggle for sale, and I came over to look at the book. As we chatted and I skimmed the text on the back cover, I became interested and bought a copy, which Mr. Guillard inscribed for me: "Keven Guillard 11/30/2017 Thanx & Enjoy Jason!!!" I took the book with me to the airport and read it on the flight home. When I got back to New York, I read the novel a second time.

For more about the book in Mr. Guillard's own words, below is an author interview I found online. For more information if you're on Facebook, here is the author's page. Finally, click here to read Amazon reviews of the book.


Saturday, April 14, 2018

Solutions to Play Your Cards Right

Reader jeff solved all of our Play Your Cards Right puzzles a while back, in fact not long after I published them. The solutions are below. Click here for all posts about puzzles of this type.


A G L: PESTS, TWINS, UDDER → PELTS, TWIGS, ADDER

B M R: COOKIE, LOOKED, STAPLE → ROOKIE, LOOMED, STABLE

A E N: CORK, CRIB, HILT → CORE, CRAB, HINT

F L X: COAT, TURN, WAIT → COAX, TURF, WAIL

A K P: SUIT, TREY, WHIR → SKIT, TRAY, WHIP

D E Y: BRAT, GOON, JUST → BRAY, GOOD, JEST

A K T: DENY, LONE, WORM → DENT, LANE, WORK

D F M: KITE, LICE, SHOO → MITE, LIFE, SHOD

H T W: DINE, GLUE, SLIM → WINE, GLUT, SHIM

I N Y: BARB, FURL, STEM → BARN, FURY, ITEM

G T Z: DUNE, RAKE, SOFA → DUNG, RAZE, SOFT

A G O: CREW, LURK, MUCK → GREW, LARK, MOCK

N P R: COVE, FLIT, HALT → CONE, FLIP, HART

L R U: PACK, SPAN, STET → LACK, SPAR, SUET

J N X: BOLD, KILT, TEST → BOND, JILT, TEXT

E W X: CLUB, FLAT, KINK → CLUE, FLAX, WINK

B C H V: LONE, SKIP, TANK, WAIT → LOVE, SHIP, TACK, BAIT

D O S V: HERE, LAZY, MITT, TALE → HERO, LADY, MIST, VALE

B H M R: DEAF, SNAG, WALK, WIND → DEAR, SHAG, BALK, MIND

D N P U V: BLUE, CLAY, LEAL, LORE, MEEK → BLED, CLAN, VEAL, LURE, PEEK

C H O L Z: BEAN, MARE, REAR, SAKE, WIDE → LEAN, MAZE, ROAR, CAKE, HIDE

G L J O P: BURY CAVE FAWN HASH RAFT → JURY, COVE, LAWN, GASH, RAPT















Saturday, April 7, 2018

Underrated and Overrated, Continued


The latest installment of our occasional feature. Now with images!

Underrated


Cottage cheese. Cottage cheese is often viewed as a problem we have to solve. The idea seems to be that cottage cheese is so nutritious that we are obligated to eat it, yet so unappealing that we'd prefer not to. As evidence, I offer this this Buzzfeed article, "30 Ways To Eat Cottage Cheese That Are Actually Delicious." The word actually gives it away: 'Actually, it's delicious! Or anyway, it can be, if you puree it with coconut, honey, and vanilla, or turn it into paneer.' Not that the Buzzfeed suggestions are bad, but my own method is much simpler: "Eat directly from the plastic tub using the largest spoon in the silverware drawer." (This method does require that you ignore the container's sour-milk smell, a problem that can also be solved by using a bowl.) The received view of cottage cheese amounts to faint praise: it's suitable for training regimens! it's safe for pregnancy! I think it's time cottage cheese got recognized as being not only nutritious, but also scarfably, squeakily satisfying.


Heist films. The Killing. Rififi. Ronin. Lock, Stock, and Two Smoking BarrelsThe Italian Job. Nine Queens. Sneakers. Jackie BrownA Fish Called Wanda. Heist. Out of Sight. Ocean's Eleven. Inception. The Sting. The bravura opening sequence of The Dark Knight. Let's even include The Hobbit, which is a heist film if you think about it. (Somebody should make that fake movie trailer!) It's true that all heist movies have pretty much the same plot, but it's a good plot that allows for a long buildup of tension, plenty of action, and various depths of human interaction. And controlling for plot makes the direction, cinematography, and other elements of the film easier to notice. Some heist films are overrated (nobody needs to watch The Usual Suspects more than once), but for my taste the genre as a whole gets too little production annually. I'm always on the lookout for the next great heist film.


Seven-card stud. It seems nobody plays seven-card stud anymore. It's a good social game, because the pace allows for a lot of table talk, especially at a table with experienced players who frequently fold. And for those remaining in the hand, the game is challenging because there's so much information to observe, remember, and make use of. Alas for that same reason, it takes a long time to become skilled at seven-card stud. People nowadays seem to prefer Hold 'Em's shorter learning curve, as well as its faster rounds, simpler data set, and more scripted play.






The Princess and the Frog. Tiana gets way too little love in comparison with her fellow Disney Princesses Elsa, Belle, Ariel, et al. It's unfair, because she's a great character and role model. The songs in The Princess and the Frog are all wonderful, and there are many nice homages to New Orleans. As much as I loved some of the songs in Frozen, the thought of watching Frozen again gives me a twitch in my left eyelid—but I'd rewatch The Princess and the Frog anytime. Here's one of its numbers, "I've Got Friends on the Other Side," sung by a charismatic voodoo-man.




Overrated


Dinosaurs. With all the excitement about dinosaurs, you'd think they were extraterrestrials. Some reptiles were larger in the past…big deal! Call me when they find out dinosaurs had ESP. (Which would probably mean that modern reptiles also have ESP.) All animals are interesting; dinosaurs are animals; ergo, dinosaurs are interesting. That's as far as I'll go.


NASA. The Curiosity rover was brilliant, but it was five years ago. What has NASA done lately? I see press releases about the International Space Station (boring), space walks (boring), education (good but still not core mission), and climate science (NOAA does it better). From what I can tell, the Mars plan is NASA's current splashy thing, yet the plan looks pretty anemic: "Send humans to orbit Mars in the early 2030s." That's twelve more years of small-ball leading to something that's still short of putting Americans on Mars! Low energy, NASA.



Bacon. The love of bacon in the U.S. verges on mass hysteria. Isn't restaurant bacon usually bad—either too dry or too fatty? Bacon also isn't much good for home cooking; unlike pancetta, say, bacon is heavy-tasting and upsets the flavors of a well balanced dish. As for bacon desserts, I believe they must have been invented by people so tired of life, so numb to experience, that they could no longer derive pleasure from a perfect warm pastry or a cold dish of ice cream. Admittedly I haven't tried any bacon desserts, because every once in a while I try to remember that meat comes from killing. Bacon desserts are frivolous; they disrespect the animal.


Rooftop bars. I owe this observation to reader Eric, and he's dead right. Rooftop bars are tacky in the same way that rotating restaurants, Benihana, and singing waiters are tacky. The view from a rooftop bar can be nice, but it's possible to enjoy a view without being exposed to the elements. And the view has to be balanced against the many aesthetic drawbacks: the ratty furniture, the chunky stemware, and—most importantly—the overpriced, poorly mixed drinks. There are several breezy weeks in Spring when being outdoors is everything: a rooftop bar makes sense then. But at other times, I'd rather drink in a smart lobby bar, a Bowery dive, or a dark tavern.


Tapas. Another just observation, this one from reader Amy. Her case is that although tapas make excellent sense in Spain, they don't make much sense in the U.S.—certainly not to the extent that would justify their popularity. Here are her arguments (emphasis in the original):
First, they are too small. Why do you need to pay more for portion control? Food shouldn’t remind you of Honey I Shrunk the Kids. Second, related to point 1, they lead to too many dishes. Tapas creates a dishes tornado. Too many plates and bowls for all those little bites. The whole ordeal (and it’s an ordeal; you can’t just grab a tapa) is served too late. Traditionally, tapas are for people who need to eat before going to to discotheque, not for people who aim to be in bed by 10pm. They are also too expensive. In Barcelona, tapas cost a few bucks a serving. In New York, for the novelty, you can easily pay $10, $15 per tapa. Why pay more for less?  

Pablo Picasso. To begin with, Cubism itself is overrated—it's ugly and abstruse. I've spent time in the Lauder Wing of the Met, and my conclusion is that Mr. and Mrs. Lauder spent way too much of their fortune on a representational dead-end. As for Picasso in particular, in the much-hyped 2015–16 exhibition of his sculpture, I saw not a single piece that I'd rank among the top fifty sculptures in the Met's permanent collection. Picasso created plenty of great works, but to be fair about it, one should also recognize how greedily this man repackaged African art for European audiences. Walk through the African rooms of the Met someday, and you might be just as surprised as I was by all the "Picassos" there. Great artists steal, I know, and my complaint really isn't about Picasso the man; I just wish Picasso's deep creative debt to Africa were more widely appreciated by the public. Picasso: a great artist, and an overrated one. [Updated 4/17/2018 to focus my Africa point more narrowly on the way people think about Picasso.]