Sunday, Fun Day (#2)

Sundays I like to post something fun in a puzzle or recreational math line. This starts a little slowly but I do get to some numerological relevance after a build-up, so bear with me if you like that sort of thing ...

The past week saw the United States finally and belatedly coming into compliance with the Jerusalem Embassy Act of 1995, with President Trump’s order to move the American Embassy in Israel to that country’s capital in Jerusalem. 

The aforementioned law, which stipulated that half the State Department’s funding should be forfeited starting in 1999 until they moved our embassy to Israel’s capital, in accordance with usual custom and common sense. In spite of the Act’s passage by wide margins (374-37 in the House, 93-5 in the Senate), the embassy remained unmoved and the State Department saw no inconvenience as a result.

The last of the five Senators who had voted Nay departed the Senate in 2010. That was Robert Byrd, the notorious former Klansman Democrat from West Virginia, who left the Senate upon his death that year, R.I.P.

The date of the Trump announcement is foretold numerologically in the cube root of the year, 2010, when the last Senate opponent to the 1995 bill left office. That cube root is 12.6 2017.

Soon it will be 2018 A.D., but the Hebrew calendar has a different numbering system for the year that started in September. To find it, write 2018. On the next line, copy the 8 below:

2  0  1  8

__ __ __ 8

Then take the digit you just wrote (8) subtract the digit above and to the left, and write that in the next spot. Eight minus one is seven:

2  0  1  8

__ __ 7  8

Continue. Seven minus zero is seven. Seven minus two is five.

2  0  1  8

5  7  7  8

And the Hebrew calendar year is 5778.

This is a triangular number, by the way. (The spirit of Dr. Matrix explained those in this post.) Perhaps President Trump is moved to support Israel’s capital this way because of an affinity with the current Jewish calendar year, since Trump is the 45th President, elected in 2016, and 45 and 2016 are also triangular numbers.

There is a simple test for whether a given number is triangular, which I “discovered”. (It’s not deep mathematics or anything, but I’ve never seen it published.) Take the number, double it, add 0.25, take the square root, and subtract 0.5. If the result is a whole number, the original number was triangular. Applying this to 5778 gives 107, so 5778 is the 107th triangular number: it is 1+2+3+...+105+106+107.

I’ll close with an original seasonal puzzle for the stout-hearted: if you’ve read this far you’re probably a mathie like me. The letters in MERRY CHRISTMAS each stand for a digit, the same letter for the same digit throughout. So MERRY is a five-digit number and CHRISTMAS is a nine-digit number, and the R’s stand for the same digit wherever they appear, as do the S’s and so on. (The word for this kind of puzzle is "cryptarithm".) So here is the puzzle, and it's a tough one: If MERRY is a perfect square and CHRISTMAS is a triangular number, what are the numbers?

Sunday, Fun Day

Reading: DRACULA, for the first time. Astounding Frontiers #2. I’m torn: I want to read John C Wright’s NOWHITHER straight through, and it’s serialized. So I’m skipping it until more of it comes out, though it hurts.

Writing projects underway:
“The Kings of the Corona”: 17000 word story: finished, accepted for the upcoming anthology TALES OF THE ONCE AND FUTURE KING, edited by Anthony Marchetta. Publication date not yet scheduled. Anthony showed us a draft of the cover art, by Dawn Witzke, and it looks great. Probably not long now. #Fantasy #Arthurian #YoungAdult
“The Stowaways” (working title) projected as 8000 word story, or maybe 6000 if I can whittle it down: work in progress. I have about 3000 words so far. #ScienceFiction #SpaceOpera




My weekends these days are mostly taken up with work connected with closing Mom’s estate, but I want weekends to be fun days. Here are a joke and a number curiosity.

A Joke

Remembered this old chestnut this afternoon. Modified it slightly:

A young man in the heart of the South wanted to instill his love of his region’s history in his young son, and walked through the park with him one day to the statue of Stonewall Jackson, flourishing his saber, mounted on his horse, frozen in a tableau of dramatic action.

“That, son, is Stonewall Jackson,” he said.

“Wow!” said the little boy.

The statue at once became the boy’s favorite spot in the park. His father noted with pride as the years passed that his son would still return there every Sunday to admire the memorial.

At last the boy graduated high school, and was about to set off for college far away. He and his father went for one last walk through the park to visit their favorite statue one more time, and they stood in silence paying their respects to it.

When they turned to go home again, the young man said, “Dad, I’ve always wondered something.”

“What is it, son?”

“Do you happen to know—who is that man with the funny beard sitting on Stonewall Jackson?”



Recreational Math

Here’s an arithmetical curiosity I noticed that has a pretty good “gee whiz” factor.

It begins with a pleasant little “find the number” puzzle: There is only one number (not counting 1, which is rather a ‘degenerate’ solution) that has this property: it is the product of the first and last digits of its square. Find the number.

To clarify the idea, if you’re not used to how I put these things (so few people are!), if you were to try the number 17 you would square it, 17 x 17 = 289, and then multiply the first and last digits, 2 times 9 = 18. We were hoping to get our 17 back: nope, close but no cigar. In case you want to try finding it, see Answer 1 is below, not to be confused with Answer 2 below.

For a second puzzle, kick the idea up a notch by taking two digits at a time: Find a number that is the product of the 2-digit number at the left and right ends of its own square.

Again, to clarify: if you were testing 2,656, you would square it: 2,656 x 2,656 = 7,054,336. Then you would take the two-digit numbers from the left and right of the square and multiply, hoping to get your 2,656 back: 70 x 36 = 2,520. Nope.

I would think you’d want to use mechanical help to work on this one. A spreadsheet is quite adequate, and it’s a nice little exercise in writing formulas.

The interesting thing is that the one number that answers this puzzle has a curious relationship with the number that worked in the first puzzle.

Okay, you've looked at the answers? Now here's what puzzles me, and I don't have an answer: Why in the world would the numbers that answer the one-digit and two-digit problems have this pattern, where the two-digit answer just repeats the digits of the one-digit answer twice? Perhaps it’s just a coincidence, or maybe there’s a mathematical reason I don’t see.

And no, repeating digits three times doesn’t work for the 3-digit version of the same puzzle.




ANSWER 1: The number is 28. 28 x 28 = 784 and 7 x 4 = 28.





ANSWER 2: The number is 2,288. 2,288 x 2,288 = 5,234,944, and 52 x 44 = 2,288.

Dr. Matrix explains 2016

The year just ended seemed so, well, odd to me that I felt a need to get some insight on it from the spirit world. I had lately learned a system for consulting with the souls of the departed, so I gave it a try. Not to bore you with the details of preparing for the seance, in a few hours I found myself in conversation with a spirit who identified himself as Dr. Irving Joshua Matrix.

"Dr. Matrix!" I exclaimed. "I thought you were a fictional creation of the late, great Martin Gardner!"

Martin Gardner wrote a series of esays recounting his interviews with Dr. Matrix over a period of many years from the 1960s to the 1980s. Dr. Matrix was a numerologist and always explained contemporary events through numerical coincidences. His theory was that numbers control human behavior, in some mystical way.

"Well, here I am," he (it?) said. "You wanted to ask something about 2016?"

"Of course. I mean, what's with Pokemon Go? And clown attacks? And how does who can go to which bathroom in North Carolina become a national issue? And..."

"My time is limited, you know. Maybe you should prioritize?"

"Well...how does the Republican party come to nominate a candidate that past Republican presidents wouldn't endorse, and whose nominating convention prominent Republicans wouldn't even attend?"

"That's more like it. You know the GOP was founded in 1854, right?"

"Um, yeah, sure, I knew that."

"Making it 162 years old in 2016. You'll note that 2016 is a shuffling of the digits of 0162, leaving no digit in the same position. Hence, the shuffling of the power within the party."

"Holy cow! I would never have thought of that! But then, how did Trump come to win out? Everyone seemed to think Hillary Clinton would win."

"Hillary was overconfident," he said, smirking. How I could tell that a disembodied spirit was smirking I can't say, but I could. "I'm afraid her numerologists were not as competent as I would have been." Hillary Clinton used numerologists? I thought. "They were deceived into thinking 2016 would be auspicious for her by the somewhat remarkable fact that 2016 times 81833 turns out to contain all the digits from 1 through 9, each one exactly once."

"Uhh," I said, whipping out my calculator. I punched in the product and found it to be 164,975,328. "Yep, all nine digits. But so what? What was that 81,833 about?"

"Translate the letters HRC, her initials, into their positions in the alphabet," explained the spirit patiently. "H is letter 8, R is 18, C is 3. So HRC is 8183, and if you repeat the last 3, there you are."

"Huh," I said. "Well."

"But what they neglected to consider is that an even more significant product is to multiply 2016 by 818330, so that you get all ten digits in the result. And that suggests HRC 30. You see?"

"Umm," I said, not seeing. "But the alphabet has only 26 letters?"

"Good lord. Don't you know the significance of the number 30 in journalism? You put it at the end of a story. It lets the next person handling the paper know that he's at the end."

Light dawned. "You mean..."

"Absolutely. 2016 marks THE END of HRC's political career."

Somehow, he seemed to be making sense. "But why Trump, of all people?"

"Well, 2016 is something new in American politics. This is, of course, the first election year in US history that's a triangular number."

"A triangular number? Let's see, that is..."

"You call yourself a math major? A triangular number is a sum of consecutive integers starting with 1. Such as 1 itself, 1+2=3, 1+2+3=6, and so on. Fifteen pool balls form a perfect triangle at the start of a game because 15=1+2+3+4+5, and those are the numbers of balls in the five rows of the triangle."

"I see," I said. "And 2016?"

"Is the 63rd triangular number. Hence the departure from previous trends, such as the GOP nominating a candidate whose last name did not have either 6 or 4 letters."

"Wait, now--what's that about?"

"Great Gauss's ghost, you really are a beginner, aren't you? You haven't noticed that ever since the Watergate scandals, every GOP presidential candidate's first and last names have had either 6 or 4 letters?"

"What? Wait a minute," I said. How could anything so bizarre have escaped notice? Let's see: Gerald Ford; Ronald Wilson Reagan, George Bush -- two of those -- Robert Dole, John McCain, Mitt Romney: holy guacamole, he's right!

"But what could account for that?" I said, baffled.

"Gerald Ford set it off, of course. The Republicans were so relieved to be done with Watergate, and FORD suggested F or D, which translated to their alphabet positions, meant 6 or 4. The trend held for nearly 40 years. It even affected most of their vice presidents. Up until the overwhelming influence of the triangular number, 2016, when you elected the 45th president: 45 being the 9th triangular number. Hence, Donald John Trump, whose name has 15 letters..."

"The fifth triangular number!"

"Now you've got it. It didn't hurt that 2016 divides into 20 and 16, which are the positions of T and P in the alphabet, the first and last letters of his name.

"Of course, once he got the nomination it was practically over, since 2016 is pretty obviously a Republican year, based on its remainder when divided by 17. Since 1968, every election year whose remainder when divided by 17 was from 1-7 has had a Democrat president, and all others Republican."

My head was spinning by this time. "Then--then, for instance, that's how Barack Obama won reelection in 2012? It was fated all along? I mean, even Karl Rove was flabbergasted--"

The spirit snorted. Imagine something that could make a spirit snort. "Of course he won in 2012. It's four times 503, a prime number. The Democrats haven't lost an election in a year that was four time a prime since Reconstruction. I mean, if people would pay attention to just rudimentary numerology--"

"Okay, hang on. What can you tell me about 2017?"

"Twenty-seventeen, now that's when things are going to get really interesting," he said, but his voice seemed to be coming from farther away. "You see ..."

It was as if he were retreating down a hallway. "Dr. Matrix!" I cried. "Talk louder! I can't hear!"

I could still make out his voice, but only snatches of words now. "... prime ... expressed in base ... cube root ..."

And that was all.