Question and Answer thread

[gwnn]

Sometimes I run into a question that is very hard to Google. Then sometimes I try Yahoo Answers and people are always eager to help but often they're quite useless. So I'm thinking maybe there's some possibility of creating a place here where people can ask and answer questions. After all, we're all thoroughly intelligent people from a vast variety of backgrounds.

[gwnn]

What was that game called where you had to conquer little squares inside a big square? Say there's a 10x10 field then at each turn you would draw in one of the 180 interior lines. If you complete one of the 100 squares, you fill it with your sign (X or O) and you'd draw another line.

 

Usually you would draw the lines at random and avoid to concede any little squares, but then after a while you'd be forced into conceding and then your opponent would win almost 100-0.

[kenberg]

I think that this is (essentially) what Elwyn Berlekamp calls, not surprisingly, the Dots and Boxes game. As he describes it, there are only dots at the outset so the outer box also hast to be completed.

 

See:

The Dots and Boxes Game

Sophisticated Child's Play

A K Peters (Publisher)

2000

[gwnn]

thanks! yes the only difference was that we always drew a box first.

[Elianna]

We always played it without the outer box as well.

[nigel_k]

Also played it without the outer box and it would not be 100-0. Someone would eventually get some squares, then have to give the other player some squares, etc. No idea what the name is, I think we just called it squares.

[mohitz]

Don't want to ruin the thread but in case people haven't heard, there is a great new startup www.quora.com for Q&A. I have found it to be very useful.

[WellSpyder]

Don't know why, but to us it was called "orange boxes".

[Trinidad]

Don't know why, but to us it was called "orange boxes".

In Dutch it is called "kamertje verhuren" (="letting rooms"), obviously because you are partitioning of the plane in small rooms.

 

Rik

[BunnyGo]

For anyone interested in winning this game, check out "Winning ways for your mathematical plays." Additionally, one of the authors has also written another book exclusively about how to play the game.

[Winstonm]

Who is Bill Buckner?

 

If you are 12-years-old and watching ESPN Classics with your dad, this is a question. If you are a contestant on Jeapordy, it is an answer.

 

So much for the Law of Non-Contradiction.

[USViking]

Who is Bill Buckner?

 

If you are 12-years-old and watching ESPN Classics with your dad, this is a question. If you are a contestant on Jeapordy, it is an answer.

 

So much for the Law of Non-Contradiction.

 

Is this the same Buckner who was playing 1B for the Boston Red Sox

with two out in the bottom of the 9th of the 6th game of the 1986

World Series?

 

If so he let a ground ball get past him on what would have been the

final out of series, since the Red Sox had a 3-2 lead in games.

The error allowed the NY Mets to first tie the game and then win it.

The Mets followed up by winning the final game the next day, and the

Curse of Babe Ruth remained in effect for another 18 years.

 

Red Sox manager John McNamara was criticized for leaving Buckner,

a poor fielder, in the game when a better fielder was available

to substitute.

[USViking]

Is this the same Buckner who was playing 1B for the Boston Red Sox

with two out in the bottom of the 9th of the 6th game of the 1986

World Series?

 

If so he let a ground ball get past him on what would have been the

final out of series, since the Red Sox had a 3-2 lead in games.

The error allowed the NY Mets to first tie the game and then win it.

The Mets followed up by winning the final game the next day, and the

Curse of Babe Ruth remained in effect for another 18 years.

 

Red Sox manager John McNamara was criticized for leaving Buckner,

a poor fielder, in the game when a better fielder was available

to substitute.

Son of a gun I garbled the story.

 

I got Bill Buckner right and also the teams, the year and the Series game number,

but I got the inning wrong (it was the 10th) and the score wrong (it was tied) and

the result of the error wrong (it let in the winning run).

 

 

Here is another famous World Series name from a generation before Bill Buckner,

also involving the Red Sox:

 

Who is Enos Slaughter, and describe the play which made him famous.

[mycroft]

I don't know, but he was definitely part of a classic (not The Classic, though) Abbott and Costello sketch (along with the fella', whose name was Feller). "Well, maybe 'e knows Slaughter, but I don't!"

[USViking]

I don't know, but he was definitely part of a classic (not The Classic, though) Abbott and Costello sketch (along with the fella', whose name was Feller). "Well, maybe 'e knows Slaughter, but I don't!"

 

I thought you were pulling my leg until I googled the quote, and it checks out.

 

I did not realize that the routine "Who's on First?" was an Abbott and Costello production.

 

Getting back to the question I posed, the St. Louis Cardinals' Enos Slaughter was on first

base with two out and the score tied in the bottom of the 8th inning in Game 7 of the 1946

World Series vs the Boston Red Sox.

 

He took off with the pitch on a hit and run play. The batter made a hit to the outfield.

The outfielder who handled the ball bobbled it slightly and then made a weak throw to the

shortstop, who had to go to the shallow outfield to take the throw. Most runners in Slaughter's

postion whould have been content to stop at 3rd, especially with the 3rd base coach singalling

them to stop. Instead, Slaughter ignored the coach, rounded the base, and headed for home.

The shortstop, astounded by Slaughter's action, made a poor, short throw to the catcher,

and Slaughter scored what proved to be the winning run of the game and Series.

[gwnn]

what's an indestructible number?? I tried google and it doesn't help

[kenberg]

what's an indestructible number?? I tried google and it doesn't help

 

 

http://www2.research.att.com/~njas/doc/g4g8.pdf

and scroll down near bottom of page 2 for power train.

 

Here is a typical map:

3452->3^4 X 5^2=81 X25=2025

and

2025->2^0 X2^5=32

But then

2592->2^5 X 9^2=32 X 81=2592, a fixed point under that mapping.

 

Generally abcd...->a^b X c^d X..., and if there are an odd number of digits you just use it without an y exponent.

 

 

Of course a,b,c,... are base ten digits and so we could do the analogous thing in any other base.

[babalu1997]

http://www2.research.att.com/~njas/doc/g4g8.pdf

and scroll down near bottom of page 2 for power train.

 

Here is a typical map:

3452->3^4 X 5^2=81 X25=2025

and

2025->2^0 X2^5=32

But then

2592->2^5 X 9^2=32 X 81=2592, a fixed point under that mapping.

 

Generally abcd...->a^b X c^d X..., and if there are an odd number of digits you just use it without an y exponent.

 

 

Of course a,b,c,... are base ten digits and so we could do the analogous thing in any other base.

 

what was paris hilton wearing when she was made to clean up graffotti?

[gwnn]

http://www2.research.att.com/~njas/doc/g4g8.pdf

and scroll down near bottom of page 2 for power train.

 

Here is a typical map:

3452->3^4 X 5^2=81 X25=2025

and

2025->2^0 X2^5=32

But then

2592->2^5 X 9^2=32 X 81=2592, a fixed point under that mapping.

 

Generally abcd...->a^b X c^d X..., and if there are an odd number of digits you just use it without an y exponent.

 

 

Of course a,b,c,... are base ten digits and so we could do the analogous thing in any other base.

I don't see the word "indestructible" anywhere. :)

[kenberg]

I don't see the word "indestructible" anywhere. :)

 

Good point. Numbers are indestructible if they don't get destroyed by the mapping.

24547284284866560000000000 ->

2^4 X 5^4 X 7^2 X 8^4 X 2^8 X 4^8 X 6^6 X 5^6=

24547284284866560000000000

 

so 24547284284866560000000000 is indestructible. (0^0=1 by definition).

 

As Wyman notes at http://www.bridgebase.com/forums/topic/44687-interesting-numbers/

there is no a priori reason why numbers cannot cycle w->x->y->z->w and maybe some do. Maybe they should be called resurrectable.

 

It's a feature of the definition that single digit numbers are indestructible but that's sort of like 1 being, or not being, prime. The two known non-trivial ones are 2592 and 24547284284866560000000000

 

Caveat: I never heard of indestructible numbers before the post about the Bello book. So I am parroting what I have found out.

 

Note: If anyone says "Who cares?", the answer is probably no one cares all that much. Mathematics as a whole is important, and sometimes a seemingly uninteresting result can be surprisingly useful, but I think that in this case we do not have to worry if another country is ahead of us in the theory of indestructible numbers.

[y66]

Deleted -- too general

[mycroft]

Ken, is an "indestructable" number only one that is fixed under the powertrain mapping, or is a number "indesctructible under mapping M(f)" if M(x) = x? If so, does the term apply to any generic set element under a mapping of element type to the same element type?

[kenberg]

Ken, is an "indestructable" number only one that is fixed under the powertrain mapping, or is a number "indesctructible under mapping M(f)" if M(x) = x? If so, does the term apply to any generic set element under a mapping of element type to the same element type?

 

So the first answer is: I don't know. I first heard of indestructible numbers by reading the "interesting numbers" thread and following up by googling Below and Conway on it all. So I don't know nothin.

 

But I am not sure that I understand your question. Yes I am (reasonably) sure that the term is context specific, meaning that Conway or Bello or one of those guys invented it to deal with numbers arising in some manner from the powertrain map. I say this just on a general feel for how terms like this come into being. Sometimes it seems there is a gnome locked away somewhere making up these terms.

 

Someone recently sent me a video related to this perverse invention of words:

 

[Fluffy]

what happens to the ships traveling the Pacific when the tsunamis come to them?

[PassedOut]

what happens to the ships traveling the Pacific when the tsunamis come to them?

As I understand it, hardly noticeable in deep water--a gentle one-meter rise in water level. It's when the tsunami reaches shallow areas that the huge wall of water forms.