5984 puzzle

Anyone need a nice number puzzle these days?


5984 is a factor in an interesting product. If you multiply 5984 by a certain four-digit number, ABCD, the product is BBAADDCC: The same four digits in the second number, but repeated in that pattern. Can you find the number?

Enjoy...

I’m plugging away at a third story, set mostly in a space station hovering over Saturn in the form of a “neo-Gothic” castle. I mean it to have a sense of doom and foreboding, like the first arrival in Dracula’s castle. The story’s mood is different from what I’ve attempted so far. I hope my other commitments will let me finish it this month, but ... time will tell.

Number Curiosities

The number 17772 has a property that makes it unique among five-digit numbers: it is the sum of the squares of the five two-digit numbers formed when you read its digits left to right (and cycle back at the end). That is, 

17772= 17x17 + 77x77 + 77x77 + 72x72 + 21x21

Although no other five-digit number has this property, it’s also true that there is a unique five-digit number equal to the sum of the two-digit numbers formed by its own digits reading from RIGHT to LEFT. In other words, there is a unique solution to this “ cryptarithm “ (but note that repeated digits are allowed, so different letters can represent the same digit):

ABCDE = BAxBA + AExAE + EDxED + DCxDC + CBxCB

I found the solutions to both these original problems by using a spreadsheet, and the second one particularly surprised me. Perhaps it will surprise you too.

As I mentioned a couple of posts back, my story ”The Hyland Resolution” in the anthology PLANETARY ANTHOLOGY: LUNA, has a main character who likes number puzzles, and this becomes important in an unexpected way. I hope you’ll pick up the book and enjoy my story as well as all the others!

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.