Re: Crazy maths proof
Chris Ball wrote: So, another maths exercise. I'll award a pint at the January social meet for the first correct post with the next number in the sequence, and another for an explanation of the sequence itself. 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 60 The next number is 61, then 67 These are orders of simple groups, only a newbie would be sidetracked by the whole prime numbers thing. I don't know what I'm talking about but the sequence appears in google, so it must be right. See: http://www.google.com/search?hl=enlr=ie=ISO-8859-1q=%2237+41+43+47+53+59+60%22 I love google and it loves me. -- Jonathan Peterson Technical Manager, Unified Ltd, +44 (0)20 7383 6092 [EMAIL PROTECTED]
Re: Crazy maths proof
On Sun, 8 Dec 2002, Chris Devers wrote: Consider the word wored 'chewed'. It has two personal pronouns in it -- 'he' and 'we'. Can you find a six letter word that has six pronouns it it? I figured out 'ushers' for myself, with the list provided from kake's link. Then I tried a few other things, but no luck, couldn't see any suitable runs/subsets (which is obviously necessary if you're to fitting 6 letter pairs into 6 spaces) So I asked the search engines. And http://users.tinyonline.co.uk/gswithenbank/wordtriv.htm reckons that : Ushers contains the most personal pronouns spelled consecutively within it: he, her, hers, she, and us, totalling five pronouns. Lots of other hits, only a few that are vaguely related to this problem, and nothing about 6 pronouns (personal or otherwise) in 6 letters. the hatter
Re: Crazy maths proof
On Sun, Dec 08, 2002 at 09:37:51PM -0500, Chris Devers wrote:
On Mon, 9 Dec 2002, Mark Fowler wrote:
I don't know, showing this to a load of Perl coders. Of course we're
not going to try and work it out, we're going to try and hack the
system. This is such an incitement for a script that sends all the
numbers from one to hundred thousand to the list ;-)
Surprisingly good word puzzle heard on pop radio this weekend:
Consider the word wored 'chewed'. It has two personal pronouns in it --
'he' and 'we'. Can you find a six letter word that has six pronouns it it?
Best I can find is ushers which has five.
#!/usr/bin/perl -w
use strict;
my @pronouns = qw(
I you he she we they it
me him her us them
mine yours his hers its ours theirs
);
=for repeated pronouns, which give more but still not a six
my @pronouns = qw(
Iyou he she it we you they
me you him her it us you them
mine yours his hers its ours yours theirs
);
=cut
my $pronoun_letters = join '', @pronouns;
my $words = q[/usr/share/dict/words];
my %count;
open WORDS, $words or die Couldn't find words '$words': $!\n;
while (WORDS) {
next unless /^[$pronoun_letters]{6}$/;
chomp; $count{$_} = 0;
for my $p (@pronouns) {
$count{$_}++ if /$p/i;
}
print Ding! Ding! Ding!\n$_\n, last if $count{$_} 5;
}
close WORDS;
for my $w (sort {$count{$b} = $count{$a}} keys %count) {
print Found $count{$w} in $w\n;
}
__END__
I haven't looked at Kake's code so I might've missed something.
Paul
--
Paul Makepeace ... http://paulm.com/
If a tree falls in the forest, then be careful about the slippery
slope.
-- http://paulm.com/toys/surrealism/
RE: Crazy maths proof
On Monday, December 09, 2002 10:11 AM, Jonathan Peterson [SMTP:[EMAIL PROTECTED]] wrote: Chris Ball wrote: So, another maths exercise. I'll award a pint at the January social meet for the first correct post with the next number in the sequence, and another for an explanation of the sequence itself. 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 60 The next number is 61, then 67 These are orders of simple groups, only a newbie would be sidetracked by the whole prime numbers thing. I don't know what I'm talking about but the sequence appears in google, so it must be right. See: In case anyone is interested in what a simple group is, check out http://www.wikipedia.org/wiki/Simple_group. Google is my friend to.
Re: Crazy maths proof
Jonathan Peterson ([EMAIL PROTECTED]) wrote: Chris Ball wrote: So, another maths exercise. I'll award a pint at the January social meet for the first correct post with the next number in the sequence, and another for an explanation of the sequence itself. 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 60 The next number is 61, then 67 These are orders of simple groups, only a newbie would be sidetracked by the whole prime numbers thing. I don't know what I'm talking about but the sequence appears in google, so it must be right. See: http://www.google.com/search?hl=enlr=ie=ISO-8859-1q=%2237+41+43+47+53+59+60%22 I love google and it loves me. This site is better than google for number sequences: http://www.research.att.com/~njas/sequences/
Re: Crazy maths proof
So, another maths exercise. I'll award a pint at the January social meet for the first correct post with the next number in the sequence, and another for an explanation of the sequence itself. 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 60 Good luck, :-) - Chris. -- $a=printf.net; Chris Ball | chris@void.$a | www.$a | finger: chris@$a | Q. How do you tell an extrovert techie from an introvert techie? | A. He looks at your feet rather than his own.
Re: Crazy maths proof
On Mon, 9 Dec 2002, Chris Ball wrote: So, another maths exercise. I'll award a pint at the January social meet for the first correct post with the next number in the sequence, and another for an explanation of the sequence itself. list-moderator-hat New rule: no random guessing /list-moderator-hat I don't know, showing this to a load of Perl coders. Of course we're not going to try and work it out, we're going to try and hack the system. This is such an incitement for a script that sends all the numbers from one to hundred thousand to the list ;-) Mark. -- Mark Fowler http://www.twoshortplanks.com/ The 2002 Perl Advent Calendar [EMAIL PROTECTED] http://www.perladvent.org/2002/ a different perl module featured every day
Re: Crazy maths proof
On Mon, 9 Dec 2002, Mark Fowler wrote: I don't know, showing this to a load of Perl coders. Of course we're not going to try and work it out, we're going to try and hack the system. This is such an incitement for a script that sends all the numbers from one to hundred thousand to the list ;-) Surprisingly good word puzzle heard on pop radio this weekend: Consider the word wored 'chewed'. It has two personal pronouns in it -- 'he' and 'we'. Can you find a six letter word that has six pronouns it it? Given that there's only a handful of personal pronouns to begin with, it seems like this should be not-too-hard, but I haven't yet figured it out. Correct answers sent to 98.5 fm in Boston by Monday will possibly get you free movie tickets or Britney Spears tickets or some such nonsense, but I think the puzzle is more interesting than the prize, personally :) -- Chris Devers[EMAIL PROTECTED]
Re: Crazy maths proof
On Sun 08 Dec 2002, Chris Devers [EMAIL PROTECTED] wrote: Consider the word wored 'chewed'. It has two personal pronouns in it -- 'he' and 'we'. Can you find a six letter word that has six pronouns it it? You utter, utter bastard. Look what you made me do: http://the.earth.li/~kake/code/pronouns.tgz It probably has some very stupid bugs in it, and/or fails to use existing modules, but it *is* the middle of the night, so I just used what was already in my brain. There are also probably many possible optimisations[0], but since computers don't need to sleep I thought I'd offload the burden in the hope that it might hit on the right answer before teatime. I'm only posting this because someone else might be able to use what I've done to make a decent solution; I have very little hope of the process I've left running coming up with anything useful. Given that there's only a handful of personal pronouns to begin with, it seems like this should be not-too-hard, but I haven't yet figured it out. I googled for pronouns and found http://www.uottawa.ca/academic/arts/writcent/hypergrammar/pronouns.html which lists 19 personal pronouns (and is where PronounList.pm in the tarball came from). 19! is big. Oh, look, nearly morning. Kake [0] One performance hit that comes to mind is that there are many many permutations that start off with the same two words that merge to a string longer than 6 characters. As it stands the code has to check each of these individually. Another is that pronouns which are substrings of other pronouns (eg she, he) aren't treated specially.
Re: Crazy maths proof
On 2002-12-02 21:40:47, Paul Makepeace [EMAIL PROTECTED] said: I should point out I was shooting for first post to get it in before Shevek, Tony, Chris et al rather than any real attempt at technical accuracy :-) :-) Why, I'm honoured to be included with such eminent mathematicians[1]. I'm only a lowly CS undergrad. :-) P (I think it's right though...) Me too. Another common feature of these sorts of puzzles is tricking you with a division error or something. This one took me longer than it should have done: (with lame markup from the original left intact) == assume two numbers a b, where a = b. step 1: a = b step 2: a2 = ab [ after you multiply both sides by a ] step 3: a2 - b2 = ab - b2 [ subtract b2 from both sides ] step 4: (a + b)(a - b) = b(a - b) [ factor both sides ] step 5: (a + b) = 1b [ divide both sides by (a - b) ] step 6: 2b = 1b [ since a = b, (a + b) = 2b ] step 7: 2 = 1 [ after you divide both sides by b ] == - Chris. [1]: You were talking about me rather than another Chris, right? :-) -- $a=printf.net; Chris Ball | chris@void.$a | www.$a | finger: chris@$a | We just typed make -- Stephen Lambrigh, Director of Server Product | Marketing at Informix, about porting Informix to Linux.
RE: Crazy maths proof
: assume two numbers a b, where a = b. : : step 1: a = b : step 2: a2 = ab [ after you multiply both sides by a ] pffft but it did confuse me for about 10 minutes. --cal ** For great Emap magazine subscription gift offers visit http://www.emapmagazines.co.uk ** The information in this email is intended only for the addressee(s) named above. Access to this email by anyone else is unauthorised. If you are not the intended recipient of this message any disclosure, copying, distribution or any action taken in reliance on it is prohibited and may be unlawful. Emap plc and or its subsidiaries do not warrant that any attachments are free from viruses or other defects and accept no liability for any losses resulting from infected email transmissions. Please note that any views expressed in this email may be those of the originator and do not necessarily reflect those of this organisation.
Re: Crazy maths proof
On Tue, 3 Dec 2002, Chris Ball wrote:
On 2002-12-02 21:40:47, Paul Makepeace [EMAIL PROTECTED] said:
I should point out I was shooting for first post to get it in
before Shevek, Tony, Chris et al rather than any real attempt at
technical accuracy :-) :-)
Why, I'm honoured to be included with such eminent mathematicians[1].
I'm only a lowly CS undergrad. :-)
I'm a what?
I'm thinking the best explanation is that Any instance of the original
formula for a given x is only true exactly at that x anyway. so the whole
thing doesn't make a lot of sense. The x + .. + x = x^2 is not a
functional equality, it's simply a statement that For a given y, x*y=x^2
at x=y and only there. So the whole differentiation thing makes no sense.
step 1: a = b
step 2: a2 = ab [ after you multiply both sides by a ]
step 3: a2 - b2 = ab - b2 [ subtract b2 from both sides ]
step 4: (a + b)(a - b) = b(a - b) [ factor both sides ]
step 5: (a + b) = 1b [ divide both sides by (a - b) ]
= 0, as we all know.
step 6: 2b = 1b [ since a = b, (a + b) = 2b ]
step 7: 2 = 1 [ after you divide both sides by b ]
S.
--
Shevek
I am the Borg.
sub AUTOLOAD{my$i=$AUTOLOAD;my$x=shift;$i=~s/^.*://;print$x\n;eval
qq{*$AUTOLOAD=sub{my\$x=shift;return unless \$x%$i;{$x}(\$x);};};}
foreach my $i (3..65535) { {'2'}($i); }
Re: Crazy maths proof
On Mon, Dec 02, 2002 at 08:46:32PM +, Earle Martin wrote: and in general: x + x + . + x = x^2 \___ x times ___/ Derive in place: 1 + 1 + . + 1 = 2 x \___ x times ___/ 1 * x = 2 x If you're going to do differentiate a function of a function in x you will another stage. The x times is obviously a function of x. Let f = u(v(x)). u(v) = v^2; v(x) = x Using the chain rule, du = du . dv = 2v . 1 = 2x dx dv dx Note the formula is valid for pure fractionals too, for example: 0.05 + 0.05 + 0.05 + 0.05 + 0.05 = 0.01 * (5 + 5 + 5 + 5 + 5) = 0.01 * 5^2 = 0.05 ^2 = 0.25 and thus it is valid for any real number x because we can always write x as a sum of a pure integer u and a pure fractional v: x = u+v. For example x=3.8 = u=3 and v=0.8. So we are not deriving in a discrete space, think somewhere else. This is totally spurious. Fear the rigor of proofs that say derive instead of differentiate and not in a discrete space, somewhere else :-) Paul -- Paul Makepeace ... http://paulm.com/ If I could have what I want, then feeble screebles. -- http://paulm.com/toys/surrealism/
Re: Crazy maths proof
On Mon, Dec 02, 2002 at 09:18:45PM +, Paul Makepeace wrote: This is totally spurious. /me sends this back to where he got the thing from in the first place. :) -- alarm in tree
Re: Crazy maths proof
On Mon, Dec 02, 2002 at 09:31:46PM +, Earle Martin wrote: On Mon, Dec 02, 2002 at 09:18:45PM +, Paul Makepeace wrote: This is totally spurious. /me sends this back to where he got the thing from in the first place. :) I should point out I was shooting for first post to get it in before Shevek, Tony, Chris et al rather than any real attempt at technical accuracy :-) :-) P (I think it's right though...) -- Paul Makepeace ... http://paulm.com/ What is that on your face? Your question shows you have learned much, Grasshopper! -- http://paulm.com/toys/surrealism/
