Persistence, Palindromes and 196

Here is a long-promised post - the "persistence of the intergers"!!!

"Peristence" is easy to define - just take a number and multiply all its digits together and continue until you are left with just one.

Example - 39. 39 becomes 3 x 9 = 27, then 27 becomes 2 x 7 = 14, and 14 becomes 1 x 4 = 4. Three steps, so the "persistence" of 39 is 3.

You can do it with any number you like. Obviously, numbers with a zero in have persistence 1, so they are not very interesting. Try finding the persistence of 6,788.

What IS interesting though is finding the SMALLEST numbers of a certain persistence. 39 is an example, and is the smallest number of persistence 3. 6,788 is the smallest of persistence 6.

That is, all numbers lower than 39 have persistence 2 or 1, and all higher than 39 have peersistence 3 or higher. For 6,788, all numbers LOWER than 6,788 have persistence 5 or less, whilst all higher have pertistence 6 or more.

Now, here's where it gets really interesting, because it is widely believed that there is absolutely NO number whatsoever with a peristence higher than 11. That, is, no number has been found to take more than 11 steps to reduce to one digit. I find this staggeriing, simply because you can invent any number as long as you like, say with 500 digits, and when you apply the persistence rule, it reduces to one digit in less than 11 steps. Try it!

Incidentally, this is just multiplicative persistence. The other one is additive persistence, where you add instead of multiply the digits, but is not quite as interesting.

Like I have said before, numbers facinate me. On a related topic, there are the palindromes, numbers like 121 and 3443 that read the same forward and backwards. If you take any number, and add it to its reversal, this produces another number. Do it again and again until a palindrome is produced. Example: 456: 456 + 654 = 1110: 1110 + 0111 = 1221 a palindrome. Try it with any number - you will eventually, after only at most 24 reversals, get a palindrome,

BUT NOT FOR 196 !!! Despite an enormous amount of computer power, 196 has still not produced a palindrome.

Nobody has the foggiest idea why 196 is special this way, but it is deeply fascinating to speculate why it is 196 and not 197 or 195, say. Try them! They both produce palindromes easily!

Watch this space for the emirps, Kaprekar numbers, and the Weird numbers!

England Soccer "Blues"!!!!!!

First, England Soccer Club had this:







He was called Emlyn "crazy horse" Hughes. (the seventies)








Then, they got this:



He was called "Gazza" and was famous for crying. (the nineties)



























NOW, in the "noughties", (or should it be said "Naughties"?) they have this:



HE is just known as "LOONEY", whoops, sorry, Rooney.

This man is almost entirely responsible for England's defeat at the hands of Portugal in the World Cup. He committed a foul by stamping on another player's Family Allowance, and then, in a fit of petulance, pushed another player out of his way so that he could argue with the referee, only a yard away!!! First foul - Yellow Card. Second foul, for just being too stupid to know better, the Red Card. I say well done referee. I bet Sven Goran had a few choice words afterwards, and maybe even a boot flew in somebody's forehead's direction. (Ask David Beckham about that one) .

The England Team consist of One Genius (Gerrard), 8 or 9 fools, and one Looney, Whoops! I meant complete Idiot! Sorry Mr Roooooney!

All in the in the Best POSSIBLE taste!

Anybody who susses all the allusions in this one gets a Green Card.

Maria Full of "Grace"? Purrlease!!!

"Maria Full of Grace"


Thursday, 29 June, 2006

...." Ever since she won Wimbledon two summers ago Maria Sharapova has become accustomed to first-class attention, even in the courts allocated for her to play on. Show courts most of the time, naturally.

Today she won her second round match against Ashley Harkleroad on Court Two, the notorious ‘Graveyard of Champions’ where many top names have crashed to defeat in the past. For Sharapova, it was more a playground than a graveyard as she romped home for the loss of four games and it brought forth a few sentimental memories.

On her Wimbledon debut as a wild card in 2003, Sharapova was beaten on Court 18 by Svetlana Kuznetsova in the fourth round. "People were walking back and forth, just like on Court Two today," she said. "But it's good, the fans can get to see up close and personal......"

....or so says journalist Ronald Atkin on the official Wimbledon website. In the picture, he says she is "trying to "suppress" her emotions" during a bout of sniffles.

What a laugh!

His Headline was "Maria full of Grace"

If it is grace she has, she ejaculates it with her every tennis shot, from her mouth, throat and her other "nether" regions. I would hardly call a pretty girl vomiting non-verbal abuse with her every "stroke" the least bit graceful.

But then again, I am just a girl myself, who cannot watch this "graceful one" because of the distrsaction she causes with the noise. I mean, it must rate close to a jackhammer on the decibel level.

Poor opponents, who actually have to face this across the net!

I must confess, I cannot recall any other sport abused in this mannner.


Give me Ping Pong anytime. I challenge anyone at that, and I don't so much as "regurgitiate" anything, not even between points, despite any sniffles!