78 Pages and More of Arithmetic Trivia About 2022

2022 is a new and, we all hope, less brutal year. It is also a number, though, an integer. And every integer has some interesting things about it. Iva Sallay, of the Find The Factors recreational mathematics blog, assembled an awesome list of trivia about the number. This includes a bunch of tweets about the number’s interesting mathematical properties. At least some of them are sure to surprise you.

If that is not enough, then, please consider something which Christian Lawson-Perfect noted on Mathstodon. It is 78 pages titled Mathematical Beauty of 2022, by Dr Inder J Taneja. If the name sounds faintly familiar it might be that I’ve mentioned Taneja’s work before, in recreational arithmetic projects.

None of this trivia may matter. But there is some value in finding cute and silly things. Verifying, or discovering, cute trivia about a number helps you learn how to spot patterns and learn to look for new ones. And it’s good to play some.

Reading the Comics, July 2, 2016: Ripley’s Edition

As I said Sunday, there were more mathematics-mentioning comic strips than I expected last week. So do please read this little one and consider it an extra. The best stuff to talk about is from Ripley’s Believe It Or Not, which may or may not count as a comic strip. Depends how you view these things.

Randy Glasbergen’s Glasbergen Cartoons for the 29th just uses arithmetic as the sort of problem it’s easiest to hide in bed from. We’ve all been there. And the problem doesn’t really enter into the joke at all. It’s just easy to draw.

John Graziano’s Ripley’s Believe It Or Not on the 29th shows off a bit of real trivia: that 599 is the smallest number whose digits add up to 23. And yet it doesn’t say what the largest number is. That’s actually fair enough. There isn’t one. If you had a largest number whose digits add up to 23, you could get a bigger one by multiplying it by ten: 5990, for example. Or otherwise add a zero somewhere in the digits: 5099; or 50,909; or 50,909,000. If we ignore zeroes, though, there are finitely many different ways to write a number with digits that add up to 23. This is almost an example of a partition problem. Partitions are about how to break up a set of things into groups of one or more. But in a partition proper we don’t really care about the order: 5-9-9 is as good as 9-9-5. But we can see some minor differences between 599 and 995 as numbers. I imagine there must be a name for the sort of partition problem in which order matters, but I don’t know what it is. I’ll take nominations if someone’s heard of one.

Graziano’s Ripley’s sneaks back in here the next day, too, with a trivia almost as baffling as the proper credit for the strip. I don’t know what Graziano is getting at with the claim that Ancient Greeks didn’t consider “one” to be a number. None of the commenters have an idea either and my exhaustive minutes of researching haven’t worked it out.

But I wouldn’t blame the Ancient Greeks for finding something strange about 1. We find something strange about it too. Most notably, of all the counting numbers 1 falls outside the classifications of “prime” and “composite”. It fits into its own special category, “unity”. It divides into every whole number evenly; only it and zero do that, if you don’t consider zero to be a whole number. It’s the multiplicative identity, and it’s the numerator in the set of unit fractions — one-half and one-third and one-tenth and all that — the first fractions that people understand. There’s good reasons to find something exceptional about 1.

dro-mo for the 30th somehow missed both Pi Day and Tau Day. I imagine it’s a rerun that the artist wasn’t watching too closely.

Aaron McGruder’s The Boondocks rerun for the 2nd concludes that storyline I mentioned on Sunday about Riley not seeing the point of learning subtraction. It’s always the motivation problem.

Reading the Comics, January 29, 2015: Returned Motifs Edition

I do occasionally worry that my little blog is going to become nothing but a review of mathematics-themed comic strips, especially when Comic Strip Master Command sends out abundant crops like it has the past few weeks. This week’s offerings bring out the return of a lot of familiar motifs, like fighting with word problems and anthropomorphized numbers; and there’s one strip that suggests a pair of articles I wrote a while back might be useful yet.

Bill Amend’s FoxTrot (January 25, and not a rerun) puts out a little word problem, about what grade one needs to get a B in this class, in the sort of passive-aggressive sniping teachers long to get away with. As Paige notes, it really isn’t a geometry problem, although I wonder if there’s a sensible way to represent it as a geometry problem.

Ruben Bolling’s Super-Fun-Pax Comix superstar Chaos Butterfly appears not just in the January 25th installment but also gets a passing mention in Mark Heath’sSpot the Frog (January 29, rerun). Chaos Butterfly in all its forms seems to be popping up a lot lately; I wonder if it’s something in the air.

Some Facts For The Day

Measure the speed of light with marshmallows http://t.co/cMbd5dSjir via @Nectarineimp

— Units (@UnitFact) April 22, 2014

I’d just wanted to note the creation of another fact-of-the-day Twitter feed from the indefatigable John D Cook. This one is dubbed Unit Facts, and it’s aiming at providing information about where various units of measure come from. The first few days have begun with, naturally enough, the base units of the Metric System (can you name all seven?), and has stretched out already to things like what a knot is, how picas and inches are related, and what are ems and fortnights besides useful to know for crossword puzzles, or how something might be measured, as in the marshmallow tweet above.

Cook offers a number of interesting fact-of-the-day style feeds, which I believe are all linked to one another through their “Following” pages. These include algebra, topology, probability, and analysis facts of the day, as well as Unix tool tips, RegExp and TeX/LaTeX trivia, symbols (including a lot of Unicode and HTML entities), and the like. If you’re of the sort to get interested in neatly delivered bits of science- and math- and computer-related trivia, well, good luck with your imminent archive-binge.

And The $64 Question Was …

I ran across something interesting — I always do, but this was something I wasn’t looking for — in John Dunning’s On The Air: The Encyclopedia of Old-Time Radio, which is about exactly what it says. In the entry for the quiz show Take It Or Leave It, which, like the quiz shows it evolved into (The $64 Question and The $64,000 Question) asked questions worth amounts doubling all the way to $64. Says Dunning:

Researcher Edith Oliver tried to increase the difficulty with each step, but it was widely believed that the $32 question was the toughest. Perhaps that’s why 75 percent of contestants who got that far decided to go all the way, though only 20 percent of those won the $64.

I am a bit skeptical of those percentages, because they look too much to me like someone, probably for a press release, said something like “three out of four contestants go all the way” and it got turned into a percentage because of the hypnotic lure that decimal digits have on people. However, I can accept that the producers would have a pretty good idea how likely it was a contestant who won $32 would decide to go for the jackpot, rather than take the winnings and go safely home, since that’s information indispensable to making out the show’s budget. I’m a little surprised the final question might have a success rate of only one in five, but then, this is the program that launched the taunting cry “You’ll be sorrrreeeeee” into many cartoons that baffled kids born a generation after the show went off the air (December 1951, in the original incarnation).

It strikes me that topics like how many contestants go on for bigger prizes, and how many win, could be used to produce a series of word problems grounded in a plausible background, at least if the kids learning probability and statistics these days even remember Who Wants To Be A Millionaire is still technically running. (Check your local listings!) Sensible questions could include how likely it is any given contestant would go on to the million-dollar question, how many questions the average contestant answer successfully, and — if you include an estimate for how long the average question takes to answer — how many contestants and questions the show is going to need to fill a day or a week or a month’s time.

Trivial Little Baseball Puzzle

I’ve been reading a book about the innovations of baseball so that’s probably why it’s on my mind. And this isn’t important and I don’t expect it to go anywhere, but it did cross my mind, so, why not give it 200 words where they won’t do any harm?

Imagine one half-inning in a baseball game; imagine that there’s no substitutions or injuries or anything requiring the replacement of a batter. Also suppose there are none of those freak events like when a batter hits out of order and the other team doesn’t notice (or pretends not to notice), the sort of things which launch one into the wonderful and strange world of stuff baseball does because they did it that way in 1835 when everyone playing was striving to be a Gentleman.

What’s the maximum number of runs that could be scored while still having at least one player not get a run?