Define the largest finite number you can in 1000 characters

Cerebral distractions of every kind, mostly but not exclusively Countdown-related.

Moderator: Michael Wallace

Post Reply
Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Tue Mar 23, 2010 4:36 pm

You have to PM your answers to me so people can't just work off other people's solutions. 1000 characters or less and see who can get the highest number. There are certain rules of course. You can't assume people have heard of numbers such as Graham's Number and use it as a starting point. In fact to keep things simple, I haven't heard of any numbers in any non-numerical form. So you have to start with these things: 0123456789 - and take it from there. I only understand +, -, * , /, ^ (power) and ! (factorial) and obviously standard use of brackets. You don't have to define your number purely using mathematical symbols. You can explain in English what you are going to do and define your own functions and numbers which you can then use.

I'm going to set the deadline for the end of next Friday (23:59 on Fri 2nd April 2010). All the answers I have I will then post in this thread and then we can discuss who wins (I don't think it will necessarily be easy to decide). If anyone uses text speak or other abbreviations to reduce the character count, then the forum can decide if what they've put is unambiguous and clear, although I will be the ultimate judge if there is disagreement. Spaces don't count in the count but you can't use the space in your definitions to make big numbers.

Any questions?

JackHurst
Series 63 Champion
Posts: 1434
Joined: Tue Jan 20, 2009 8:40 pm
Location: Leics

Re: Define the largest finite number you can in 1000 characters

Post by JackHurst » Tue Mar 23, 2010 4:47 pm

This is cool, will show it to my further maths class tomorrow morning and see if we can concoct an answer.

User avatar
Marc Meakin
Lord of the Post
Posts: 4018
Joined: Wed May 20, 2009 3:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Marc Meakin » Tue Mar 23, 2010 4:55 pm

I am not a mathemetician but would it be cheating to answer infinity minus 0. (996 further 0.s) 1.
GR MSL GNDT MSS NGVWL SRND NNLYC NNCT

User avatar
Alec Rivers
Devotee
Posts: 918
Joined: Fri Nov 14, 2008 11:36 pm
Location: Studio 57, Cheriton (Kent)
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by Alec Rivers » Tue Mar 23, 2010 5:37 pm

Gavin Chipper wrote:... I haven't heard of any numbers in any non-numerical form.
Marc Meakin wrote:... infinity ...
Sorry. :P

And anyway, that would still be infinity — a strange beast.

Howard Somerset
Kiloposter
Posts: 1955
Joined: Mon Jan 21, 2008 9:02 am
Location: UK

Re: Define the largest finite number you can in 1000 characters

Post by Howard Somerset » Tue Mar 23, 2010 5:55 pm

1000 characters is a hell of a lot.

I don't really think that the complexity of this problem is reduced at all if the maximum number of characters were to be reduced to something like 20. And I suggest that you go with that, for a start at least.

Fascinating. I first saw this thread just before starting a maths lesson, and have to admit my mind kept wandering while I was supposed to be going over the much more simple problem of quadratic factorisation. I fear that something similar will happen with my mind in the next lesson, which is about to start.

User avatar
Ian Volante
Postmaster General
Posts: 3563
Joined: Wed Sep 03, 2008 8:15 pm
Location: Edinburgh
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by Ian Volante » Tue Mar 23, 2010 7:07 pm

Yikes, we might not be able to use Graham's Number in the solution, but I wouldn't be at all surprised if the best solutions approached some noticeable fraction of it.
meles meles meles meles meles meles meles meles meles meles meles meles meles meles meles meles

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Wed Mar 24, 2010 3:16 pm

Howard Somerset wrote:1000 characters is a hell of a lot.

I don't really think that the complexity of this problem is reduced at all if the maximum number of characters were to be reduced to something like 20. And I suggest that you go with that, for a start at least.
I wasn't sure how many to pick but I think 20 is far too few. I was imagining a lot of answers would be people explaining things in English and 20 characters rules it out. I think I'll stick with 1000 and see what happens.

Oh and by the way (you know who you are), submissions have to make sense as a stand-alone answer. (It was Reams.)

I think I'm going to come up with my own as well now and PM it to myself. Just for fun :D

User avatar
Charlie Reams
Site Admin
Posts: 9447
Joined: Fri Jan 11, 2008 2:33 pm
Location: Cambridge
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by Charlie Reams » Wed Mar 24, 2010 6:33 pm

Gavin Chipper wrote: Oh and by the way (you know who you are), submissions have to make sense as a stand-alone answer. (It was Reams.)
It renders the competition a bit pointless if you change the rules after it starts.

JackHurst
Series 63 Champion
Posts: 1434
Joined: Tue Jan 20, 2009 8:40 pm
Location: Leics

Re: Define the largest finite number you can in 1000 characters

Post by JackHurst » Wed Mar 24, 2010 6:41 pm

42, beat that.

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Wed Mar 24, 2010 7:16 pm

Charlie Reams wrote:
Gavin Chipper wrote: Oh and by the way (you know who you are), submissions have to make sense as a stand-alone answer. (It was Reams.)
It renders the competition a bit pointless if you change the rules after it starts.
Only if you're a massive pedant in a case such as this (but I don't know if you're being serious, or maybe seeking revenge from times when you've perceived me to be similarly pedantic, or other).

But so other people know, the answer Charlie gave was
The largest number anyone else submits, plus one.
And if someone else submitted a similar answer it wouldn't be properly defined anyway so therefore automatically eliminated. And I haven't heard of any numbers in non-numerical form, so it's no different from saying Graham's number plus one. Also "you have to start with these things: 0123456789 - and take it from there" - I'm throwing your objection out.

User avatar
Charlie Reams
Site Admin
Posts: 9447
Joined: Fri Jan 11, 2008 2:33 pm
Location: Cambridge
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by Charlie Reams » Wed Mar 24, 2010 7:25 pm

It was really just a comment on how ill-defined your question is, which I thought would appeal to you.

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Wed Mar 24, 2010 7:34 pm

Charlie Reams wrote:It was really just a comment on how ill-defined your question is, which I thought would appeal to you.
Yeah, that's fine. The "Any questions" bit was supposed to imply I might not have defined it that clearly.

User avatar
Charlie Reams
Site Admin
Posts: 9447
Joined: Fri Jan 11, 2008 2:33 pm
Location: Cambridge
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by Charlie Reams » Wed Mar 24, 2010 7:39 pm

Gavin Chipper wrote:
Charlie Reams wrote:It was really just a comment on how ill-defined your question is, which I thought would appeal to you.
Yeah, that's fine. The "Any questions" bit was supposed to imply I might not have defined it that clearly.
Fair enough. My new answer is 640. No one will ever need more than 640.

User avatar
Neil Zussman
Enthusiast
Posts: 328
Joined: Thu Jan 15, 2009 4:41 pm

Re: Define the largest finite number you can in 1000 characters

Post by Neil Zussman » Fri Mar 26, 2010 5:39 pm

I've been thinking about this for a few days now, and I believe I've got an unbeatable answer. I hope I'm right, I've put a lot of effort into this. My answer is 639. I really think I've got this one in the bag.

User avatar
Alec Rivers
Devotee
Posts: 918
Joined: Fri Nov 14, 2008 11:36 pm
Location: Studio 57, Cheriton (Kent)
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by Alec Rivers » Fri Mar 26, 2010 6:30 pm

Charlie Reams wrote:No one will ever need more than 640.
Bill Gates [although possibly an urban myth] wrote:640K ought to be enough for anybody.
Heinrich Hertz wrote:[Electromagnetic waves are] ... of no use whatsoever.
Decca Recording Co. (rejecting the Beatles, 1962) wrote:We don't like their sound, and guitar music is on the way out.
Image

User avatar
Charlie Reams
Site Admin
Posts: 9447
Joined: Fri Jan 11, 2008 2:33 pm
Location: Cambridge
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by Charlie Reams » Fri Mar 26, 2010 7:18 pm

Popular Mechanics, 1949 wrote:Computers in the future may weigh no more than 1.5 tons.
There's another good one which I can't locate any more, something like "One day there will be a telephone in every town in America."

User avatar
Alec Rivers
Devotee
Posts: 918
Joined: Fri Nov 14, 2008 11:36 pm
Location: Studio 57, Cheriton (Kent)
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by Alec Rivers » Fri Mar 26, 2010 7:37 pm

Charlie Reams wrote:
Popular Mechanics, 1949 wrote:Computers in the future may weigh no more than 1.5 tons.
Yeah, that's a good one, too. That was amongst dozens from which I picked the Bill Gates one, including "I think there is a world market for maybe five computers" – Thomas J. Watson, 1943, Chairman of the Board of IBM.
Charlie Reams wrote:There's another good one which I can't locate any more, something like "One day there will be a telephone in every town in America."
That was Alexander Graham Bell, I believe.

craig
Rookie
Posts: 55
Joined: Thu Oct 29, 2009 5:32 pm

Re: Define the largest finite number you can in 1000 characters

Post by craig » Fri Mar 26, 2010 8:00 pm

If this thread has become funny and stupid predictions then I'll throw out...

(Margaret Thatcher) There will never be a female prime minister in my time.


If it hasn't become that then forget this post.

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Tue Mar 30, 2010 9:01 pm

OK, just a couple of days left for this. I've had a few sensible answers PMed to me but not a massive number, so it's still all to play for!

Also I was thinking of having another championship later in the year and then we can put the two winners together and have a yearly champion. But there's going to be a new calculator for 2011, so I don't want to have the play-off next year.

User avatar
Jon Corby
Moral Hero
Posts: 7987
Joined: Mon Jan 21, 2008 8:36 am

Re: Define the largest finite number you can in 1000 characters

Post by Jon Corby » Tue Mar 30, 2010 9:05 pm

Gavin Chipper wrote:I've had a few sensible answers PMed to me but not a massive number



..............WELL THEY CAN'T BE *THAT* SENSIBLE THEN CAN THEY?!!!!!!!!!!ONE!!!ELEVEN

User avatar
Matt Morrison
Post-apocalypse
Posts: 7625
Joined: Wed Oct 22, 2008 2:27 pm
Location: London
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by Matt Morrison » Tue Mar 30, 2010 9:32 pm

I tried to get this thread when it first started, and I still don't. Looking forward to seeing some answers posted here.

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Tue Mar 30, 2010 9:41 pm

Jon Corby wrote:
Gavin Chipper wrote:I've had a few sensible answers PMed to me but not a massive number



..............WELL THEY CAN'T BE *THAT* SENSIBLE THEN CAN THEY?!!!!!!!!!!ONE!!!ELEVEN
Marseille nil.

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Sat Apr 03, 2010 3:00 pm

OK, so the answers PMed to me, in chronological order:
Charlie Reams wrote:The largest number anyone else submits, plus one.
No!
Jon Corby wrote:18.
Good opening gambit but we'll have to wait and see if this can last the distance.
JimBentley wrote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
This surely takes the lead, just beating Corby. It also beats Reams's 640 mentioned in the thread.
Jon O'Neill wrote:9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9^9!
Or:
Jon O'Neill wrote:I dunno if that got truncated, but it was basically 9^ repeated 498 times, then 9!
I think this would beat Jim because as far as I understand, you automatically work backwards with ^ anyway so Jim's brackets are not required and end up as waste! More to follow.

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Sat Apr 03, 2010 3:10 pm

John Gillies wrote:9^9^9^9^9......^9!

ie 9 raised to the power 9 to the power 9 .... and finally to the power 9!

So that's 499 9's, 499 ^'s and 9! = 1000 characters
This is the same as Jon's, but interestingly they both managed to define their answers in far less than 1000 characters...
Neil Zussman wrote:Define f 0:= 9^ (9^ (9^9))
For i=1, 2, 3,…, (f0^ (f0^ (f0^ f0)), define fi+1:=fi^ (fi ^ (fi ^ fi))
Call the last of these terms g0.
For j=1,2,3,…, (g0^ (g0^ (g0^ g0)), define gj+1= gj^ (gj ^ (gj ^ gj))
Call the last of these terms h0.
For k=1,2,3,…, (h0^ (h0^ (h0^ h0)), define hk+1= hk^ (hk ^ (hk ^ hk))
Call the last of these terms w0.
Now either continue repeating the process for as long as you want. Or, calculate w0^(w0^(w0^w0)). Call this number w1. My answer is w1. Plus three and an eighth.
This was the last entry submitted. I'm not sure I 100% followed al of this, but assuming it does all make sense, it probably wins. Anyone agree/disagree? The main bit I'm unsure of is "the last of these terms".

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Sat Apr 03, 2010 3:15 pm

I started doing this myself as well but got bored before 1000 characters, as you'll see if you read on. I think if I was doing it again, I'd say about 250 or 300 (not 20 though). My answer:

Start with x (move 1) and each move is result ^ itself until move x. This gives x%. x%%%… with x %s = x (%2). x (%2)(%2)(%2)… with x (%2)s = x (%3). x(%n)(%n)… with x (%n)s = x (%n+1).

We move from x^x to x(%x) in this way using the method q-ing. We can put in x(%x) instead of x^x as the first move and q that and so on. If you q the ^ function x times you get x (^qx) x, which is x£. x£ works like x% so we can get x(£x). To get from x^x to this we have 2q-ed ^. 2q-ing is like q-ing. So by 2qing ^ x times we get x(2£) and from this we get x(2£x). Following on we have 3q-ing and xq-ing. So when we xq the ^ function we get from x^x to x$. My answer is 9$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

User avatar
Michael Wallace
Racoonteur
Posts: 5458
Joined: Mon Jan 21, 2008 5:01 am
Location: London

Re: Define the largest finite number you can in 1000 characters

Post by Michael Wallace » Sat Apr 03, 2010 3:17 pm

Gavin Chipper wrote:
Neil Zussman wrote:Define f 0:= 9^ (9^ (9^9))
For i=1, 2, 3,…, (f0^ (f0^ (f0^ f0)), define fi+1:=fi^ (fi ^ (fi ^ fi))
Call the last of these terms g0.
For j=1,2,3,…, (g0^ (g0^ (g0^ g0)), define gj+1= gj^ (gj ^ (gj ^ gj))
Call the last of these terms h0.
For k=1,2,3,…, (h0^ (h0^ (h0^ h0)), define hk+1= hk^ (hk ^ (hk ^ hk))
Call the last of these terms w0.
Now either continue repeating the process for as long as you want. Or, calculate w0^(w0^(w0^w0)). Call this number w1. My answer is w1. Plus three and an eighth.
This was the last entry submitted. I'm not sure I 100% followed al of this, but assuming it does all make sense, it probably wins. Anyone agree/disagree? The main bit I'm unsure of is "the last of these terms".
I'm not really sure it's fair to let someone get away with "for i = 1, 2, 3, ..." when you've set a character limit. But it's your puzzle, so your rules.

User avatar
JimBentley
Legend
Posts: 2781
Joined: Fri Jan 11, 2008 6:39 pm
Location: Redcar, UK
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by JimBentley » Sat Apr 03, 2010 3:55 pm

Gavin Chipper wrote:I think this would beat Jim because as far as I understand, you automatically work backwards with ^ anyway so Jim's brackets are not required and end up as waste! More to follow.
I must admit, I did wonder if the brackets were necessary and came to the conclusion that they were, but maybe I misunderstand how it works.

I thought that 9^9^9 would be (9^9)^9, or 387420489^9, whereas (9^(9^9)) is 9^387420489, which is far larger.

Entering =4^4^4 in Excel (the true arbiter of mathematical veracity, of course) gives 4294967296, but =4^(4^4) gives 1.3480 x 10^154.

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Sat Apr 03, 2010 4:06 pm

Michael Wallace wrote:
Gavin Chipper wrote:
Neil Zussman wrote:Define f 0:= 9^ (9^ (9^9))
For i=1, 2, 3,…, (f0^ (f0^ (f0^ f0)), define fi+1:=fi^ (fi ^ (fi ^ fi))
Call the last of these terms g0.
For j=1,2,3,…, (g0^ (g0^ (g0^ g0)), define gj+1= gj^ (gj ^ (gj ^ gj))
Call the last of these terms h0.
For k=1,2,3,…, (h0^ (h0^ (h0^ h0)), define hk+1= hk^ (hk ^ (hk ^ hk))
Call the last of these terms w0.
Now either continue repeating the process for as long as you want. Or, calculate w0^(w0^(w0^w0)). Call this number w1. My answer is w1. Plus three and an eighth.
This was the last entry submitted. I'm not sure I 100% followed al of this, but assuming it does all make sense, it probably wins. Anyone agree/disagree? The main bit I'm unsure of is "the last of these terms".
I'm not really sure it's fair to let someone get away with "for i = 1, 2, 3, ..." when you've set a character limit. But it's your puzzle, so your rules.
Isn't it just the same as saying f(x+1) = some function of f(x)? But it's all about whether he's clearly defined a finite number and he's said "the last of these terms" and I'm not sure he's specified a finite end point. Unless I've missed something.

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Sat Apr 03, 2010 4:11 pm

JimBentley wrote:
Gavin Chipper wrote:I think this would beat Jim because as far as I understand, you automatically work backwards with ^ anyway so Jim's brackets are not required and end up as waste! More to follow.
I must admit, I did wonder if the brackets were necessary and came to the conclusion that they were, but maybe I misunderstand how it works.

I thought that 9^9^9 would be (9^9)^9, or 387420489^9, whereas (9^(9^9)) is 9^387420489, which is far larger.

Entering =4^4^4 in Excel (the true arbiter of mathematical veracity, of course) gives 4294967296, but =4^(4^4) gives 1.3480 x 10^154.
Well, I think the real true arbiter is the Wikipedia. And it says you should work backwards (until you edit it to say otherwise).

User avatar
JimBentley
Legend
Posts: 2781
Joined: Fri Jan 11, 2008 6:39 pm
Location: Redcar, UK
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by JimBentley » Sat Apr 03, 2010 4:26 pm

Gavin Chipper wrote:
JimBentley wrote:
Gavin Chipper wrote:I think this would beat Jim because as far as I understand, you automatically work backwards with ^ anyway so Jim's brackets are not required and end up as waste! More to follow.
I must admit, I did wonder if the brackets were necessary and came to the conclusion that they were, but maybe I misunderstand how it works.

I thought that 9^9^9 would be (9^9)^9, or 387420489^9, whereas (9^(9^9)) is 9^387420489, which is far larger.

Entering =4^4^4 in Excel (the true arbiter of mathematical veracity, of course) gives 4294967296, but =4^(4^4) gives 1.3480 x 10^154.
Well, I think the real true arbiter is the Wikipedia. And it says you should work backwards (until you edit it to say otherwise).
Once again Excel betrays me. First that fucking paperclip and now this.

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Sat Apr 03, 2010 6:35 pm

Gavin Chipper wrote:I'm not sure he's specified a finite end point. Unless I've missed something.
I've read through it again and it is clear what he means actually. So I think I will declare Neil Zussman the winner.

User avatar
Michael Wallace
Racoonteur
Posts: 5458
Joined: Mon Jan 21, 2008 5:01 am
Location: London

Re: Define the largest finite number you can in 1000 characters

Post by Michael Wallace » Sat Apr 03, 2010 6:47 pm

Gavin Chipper wrote:
Gavin Chipper wrote:I'm not sure he's specified a finite end point. Unless I've missed something.
I've read through it again and it is clear what he means actually. So I think I will declare Neil Zussman the winner.
Well my point was more that by allowing someone to say "..." and use it as basically shorthand for something else seems a bit not in keeping with a character limit style problem, but I think that's just more a matter of taste/interpretation than anything else.

Edit: Although on reading it properly I see that the "..." bits are actually entirely superfluous, so then the only issue is the "as long as you want", in which case you need to just work out the furthest you can go with that sequence whilst remaining in 1000 characters.

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Sat Apr 03, 2010 7:12 pm

Michael Wallace wrote:
Gavin Chipper wrote:
Gavin Chipper wrote:I'm not sure he's specified a finite end point. Unless I've missed something.
I've read through it again and it is clear what he means actually. So I think I will declare Neil Zussman the winner.
Well my point was more that by allowing someone to say "..." and use it as basically shorthand for something else seems a bit not in keeping with a character limit style problem, but I think that's just more a matter of taste/interpretation than anything else.

Edit: Although on reading it properly I see that the "..." bits are actually entirely superfluous, so then the only issue is the "as long as you want", in which case you need to just work out the furthest you can go with that sequence whilst remaining in 1000 characters.
I decided to ignore the "as long as you want" and take his answer as "My answer is w1. Plus three and an eighth." I don't know how this compares with my answer though (if anyone can make sense of that).

David Roe
Enthusiast
Posts: 388
Joined: Mon Jan 21, 2008 12:58 pm

Re: Define the largest finite number you can in 1000 characters

Post by David Roe » Sat Apr 03, 2010 10:18 pm

You could square Jon's entry by just writing the number 9 1,000 times in formation rising diagonally up and across the page.

Difficult to do on a message board, but easy enough on paper (or on Excel).

Powers don't need a ^ symbol, after all.

Peter Mabey
Kiloposter
Posts: 1074
Joined: Sat Mar 01, 2008 3:15 pm
Location: Harlow

Re: Define the largest finite number you can in 1000 characters

Post by Peter Mabey » Tue Apr 06, 2010 8:53 pm

I considered submitting 9!!!.... (i.e factorial function applied 999 times) but find brackets need to be used to distinguish from the double factorial function, so can only get 333 repeats - probably not as good as the tower of indices. :?: :(

User avatar
Charlie Reams
Site Admin
Posts: 9447
Joined: Fri Jan 11, 2008 2:33 pm
Location: Cambridge
Contact:

Re: Define the largest finite number you can in 1000 characters

Post by Charlie Reams » Tue Apr 06, 2010 9:14 pm

David Roe wrote:You could square Jon's entry by just writing the number 9 1,000 times in formation rising diagonally up and across the page.
That's a lot more than squaring.

Hugh Binnie
Enthusiast
Posts: 290
Joined: Fri Jul 24, 2009 9:46 pm

Re: Define the largest finite number you can in 1000 characters

Post by Hugh Binnie » Thu Apr 08, 2010 8:36 am

Peter Mabey wrote:I considered submitting 9!!!.... (i.e factorial function applied 999 times) but find brackets need to be used to distinguish from the double factorial function, so can only get 333 repeats - probably not as good as the tower of indices. :?: :(
Gavin said that he understands !, not !! or !!! etc, so I think you could do that without brackets.

User avatar
Neil Zussman
Enthusiast
Posts: 328
Joined: Thu Jan 15, 2009 4:41 pm

Re: Define the largest finite number you can in 1000 characters

Post by Neil Zussman » Tue Apr 13, 2010 9:26 pm

Gavin Chipper wrote:
Michael Wallace wrote:
Gavin Chipper wrote:
I've read through it again and it is clear what he means actually. So I think I will declare Neil Zussman the winner.
Well my point was more that by allowing someone to say "..." and use it as basically shorthand for something else seems a bit not in keeping with a character limit style problem, but I think that's just more a matter of taste/interpretation than anything else.

Edit: Although on reading it properly I see that the "..." bits are actually entirely superfluous, so then the only issue is the "as long as you want", in which case you need to just work out the furthest you can go with that sequence whilst remaining in 1000 characters.
I decided to ignore the "as long as you want" and take his answer as "My answer is w1. Plus three and an eighth." I don't know how this compares with my answer though (if anyone can make sense of that).
Most of what I wrote could be written more succintly and rigorously, but I expected others to have come up with similar (and better) answers, so I didn't spend too much time working out all the details. Where I've written 'the last of these', the thing I am referring to is finite and totally ordered, so 'the last' is well defined, if not very mathematical.
I'm sure if anyone actually bothered to think about the puzzle, better answers could be found, it's a bit of a shame more people didn't put some effort in.

Gavin Chipper
Post-apocalypse
Posts: 9936
Joined: Mon Jan 21, 2008 10:37 pm

Re: Define the largest finite number you can in 1000 characters

Post by Gavin Chipper » Wed Apr 14, 2010 6:03 pm

I suppose the "best" way of doing this would be to have a formal way of defining numbers - but it would become like computer programming.

User avatar
Jon Corby
Moral Hero
Posts: 7987
Joined: Mon Jan 21, 2008 8:36 am

Re: Define the largest finite number you can in 1000 characters

Post by Jon Corby » Thu Apr 15, 2010 9:27 am

Neil Zussman wrote:it's a bit of a shame more people didn't put some effort in.

*looks guiltily down at shoes*

Post Reply

Who is online

Users browsing this forum: No registered users and 1 guest