Riddle me this! (NOT TODAY'S!!)

[Lars624]

Who else is REALLY going to MISS Cranium Command when they close Wonders of Life pavilion next year?

ME!! I really get a kick out of that show!!

It's not that I couldn't do a math riddle if it was an afternoon riddle..........just not at 6 am!!!

NO MATH....NO MATH......NO MATH

 

[oldkicker]

While digging about for riddles, I came across various references to numeric palindromes....

Count your lucky stars that I can't make a riddle out of this!

Pick a number. Reverse its digits and add the resulting number to the original number. If the result isn't a palindrome, repeat the process. Do all numbers in base 10 eventually become palindromes through this process? Nobody knows.[1]
For example, start with 87. Applying this process, we obtain:


87 + 78 = 165
165 + 561 = 726
726 + 627 = 1353
1353 + 3531 = 4884, a palindrome

In order for addition of a digits-reversed number to yield a palindrome, there must be no carries in the addition and hence each pair of digits must sum to 9 or less.

Whether all numbers eventually become palindromic under this process is unproved, but all numbers less than 10,000 have been tested. Every one becomes a palindrome in a relatively small number of steps (of the 900 3-digit numbers, 90 are palindromes to start with and 735 of the remainder take less than 5 reversals and additions to yield a palindrome). Except, that is, for 196. This number had been carried through 50,000 reversals and additions by P. C. Leyland, yielding a number of more than 26,000 digits without producing a palindrome. Later, P. Anderton continued the process up to 70,928 digits without encountering a palindrome.

On August 12, 1987, I put my Sun 3/260 to work on this problem. A program, pquest.c, performs the reversal and addition of arbitrary precision numbers and checks for a palindrome after each step. The program runs with a nice(15) priority, mopping up all available compute cycles while instantly relinquishing the CPU to normal foreground jobs. (There is no perceptible degradation in system performance when this program is running. You do have to get used to seeing your CPU meter pegged at 100% all the time, however.)

The program writes checkpoints to a file every two hours and works in conjunction with a set of shell scripts that restart it from the most recent checkpoint and shut it down with a current checkpoint when the system is being shut down. This allows the process to continue day in and day out without human intervention.

For almost three years the process of reversal and addition continued. Last night, at five minutes before midnight, the program printed the message:


Stop point reached on pass 2415836.
Number contains 1000000 digits.

and exited. The built-in endpoint had been reached; after 2,415,836 reversals and additions, 196 had grown to a number of 1,000,000 digits without ever yielding a palindrome. Does it ever produce one? Still, nobody knows. From a probabilistic standpoint, as a number grows to enormous size the likelihood of producing a palindrome on the next step decreases since the odds of a digit pair summing to 10 or more approach certainty in very large numbers. But with infinite repetition of this process...perhaps.

I will leave it at a million digits after three years of computing. The program that conducted the Quest is available for you to download. If you'd like to continue the Great Work yourself, you can download the million-digit result of the original computation so you don't have to repeat it.

What use is this? Well, none, really, but how useful is the idle loop on your computer?

I'm not planning to publish this result because after 3 years of enduring the vicissitudes of a Motorola 68020 microprocessor, I wouldn't be confident in the results without re-running them for verification and I'm not about to re-up for another 3 years. Besides, if I wait 2 years, I'll probably have a computer on my desk that can do it in 6 months--it's just like the phenomenon of slowboat interstellar travel: no matter when you leave, by the time you get there the destination is already populated by the descendants of people who left after you and traveled in faster ships built with later technology.

All of this raises a question I've been meaning to pose for some time now. Are there useful and/or interesting tasks which can be done in the background on our workstations? In particular, are there tasks which can exploit the latent supercomputer power of the idle cycles on all the Sun workstations on the Ethernet at the office in a collaborative fashion?

While these kinds of tasks have traditionally been recreational math record-busting like the 196 Palindrome Quest, I'm particularly interested in potential candidate problems more closely related to the real world such as numerical simulations of the evolution of gravitationally bound systems like globular clusters and models of galaxy formation, numerical solutions of difficult problems in quantum mechanics, and the like. I'd rather go after something like that than mount another hackneyed assault on the largest Mersenne prime.

Obviously, all such endeavours are low priority in the human domain as well as the operating system process dispatch queue.

1995 Addendum: The Crunch Goes On
In 1995, Tim Irvin, finding himself in the vicinity of a supercomputer with time on its hands, decided to carry on the Quest, starting with the million digit number I stopped at in 1990. It's indicative of progress in computing that it took just two months to carry the Quest to the two million digit mark--without finding a palindrome. Read the story of his continuation of the Quest for details. The two million digits he computed are available for you to download.

 

[The LK 4]

I didn't know that Cranium Command is closing! We loved it when we saw it in January.

I like the math riddles better because I know for sure that my answer will be correct. I don't have to make any lame guesses like "deer ticks", "flying cows" etc. and then get the dreaded IHSEIM!

 

[oldkicker]

LTM!
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[dianeschlicht]

Count your lucky stars that I can't make a riddle out of this!

If you ever pick a riddle like THAT, I will personally come over and bop you one!!!

 

[gina2000]

I love all kinds of riddles. I'm not picky.

I ESPECIALLY LOVE RIDDLES WHERE I GET PANTS!!!!! LOL LOL LOL


Today I have a sieve for a brain. No combination works. And I keep thinking they do and send in an answer.

Now THAT'S really BAD!

 

[dianeschlicht]

Today I have a sieve for a brain. No combination works. And I keep thinking they do and send in an answer.

I tried that approach at first today, too. Then I decided I better resort to algebra! I HATED algebra!

 

[love the magic]

wow....I didn't know that we were losing Cranium Command....when I was visiting last week, I made it all the way to through the pre-show, and then they asked us to leave because it wasn't operating properly....I enjoy it SO that my niece and I made a trip back to ECPOT on another day JUST to be sure we saw that....I'm glad now that I did!

 

[Lars624]

OMG Bernie!!!
PLEASE don't even think of making a riddle out of that! I think all of the riddle groupies would organize a revolt! Some sort of riddle coup would have to take place

 

[oldkicker]

Hey LK - maybe I can come up with riddles that require both!

So you can answer "4 deer ticks!" Hee hee....

Hi, Amid! I hope Norah feels better soon. Cold? Flu? Let her rest. But no rest for you! Have fun providing taxi service!

'Morning, Elaine! My Weather Bug chirps at me almost every morning. I love it when it tells me it's going to snow! Snow in February In Syracuse? WELL NO DUH!!!!

LTM - that's a great message for the kids, and us, isn't it? We are special and make a difference.

John - I think I may try to come up with some PICTURE riddles! Katie has been helping me with some. They are very silly and cute....

 

[dianeschlicht]

I think all of the riddle groupies would organize a revolt!

A BOP BERNIE coup!!

 

[helenabear]

Oh my... Bernie that made my head hurt!!

I forgot to say how much I will miss Mr. Rogers. I really will miss the good wholesome show he put on. I really wish more shows like that were out there. He definitley seemed to be one of the last of a dying breed.

I will so miss Cranium Command I thought it was such a cute show! While I missed it this last time I went (I missed a TON of rides, I admit) I always did my best to see it. I just thought it was funny and cute

 

[Debbie]

Maybe we need to count left brains and right brains here!

Today I feel like I have no brains....and just that sieve of gina's.

Add me to the chant:

NO MATH. . .NO MATH. . .NO MATH. . .NO MATH. . .NO MATH. . .

 

[oldkicker]

If I ever do make a riddle outta that, you all have my permission to BOP me!

........

 

[paras4ri]

Gina - DS loved Shining Time Station too....we still have a Thomas train set that I can't bear to part with. Now I'm humming the song - thanks!

My vote is
NO MATH!!!!!!!!!!!!!!!!!!!!!

Have a great day everyone!

 

[oldkicker]

Pay no attention to that man behind the curtain....

 

[The LK 4]

So if the wife gives her husband a deer tick and then they have the same amount of deer ticks, but if he gives her a deer tick and then she has twice as many as he does, how do they get rid of them?

 

[dianeschlicht]

Now HOW am I supposed to comment on a generic curtain like THAT, Bernie??? I suppose it does look a little like a geometry problem. Oh no!!! A MATH shower curtain!!!

 

[Credit Man]

Good morning fellow riddlers! PM sent.

 

[yepod]

Originally posted by oldkicker
Count your lucky stars that I can't make a riddle out of this!

You'll be COUNTING stars, Bernie