Poll on Coulter.

[molly bloom]

Originally posted by Kuciwalker


Maybe we should be more like Aristotle's lyceum: just math and philosophy

http://www.cals.ncsu.edu/agexed/aee501/aristotle.html

'All students were assigned tasks involving historical or scientific research. Aristotle based many of his scientific propositions upon this research.'

http://www.edst.purdue.edu/georgeoff/EDFA_200/Aristotle.htm

'Although study at the Lyceum seems to have concentrated on rhetoric and logic, a shift shortly was made to the natural sciences, resulting in a curriculum distinctly different from Plato’s Academy.'

Including but not limited to, zoology, marine biology, cosmology, taxonomy, Aristotelean (non-mathematical) logic....

http://people.bu.edu/wwildman/WeirdWildWeb/courses/wphil/lectures/wphil_theme03.htm

'Aristotle’s Lyceum

Founded in 335, close to Athens, when Aristotle was 49
Curriculum emphasized natural science; contrast with Academy’s stress on mathematics, and speculative and political philosophy. '

[Kuciwalker]

20101?

Thanks, jag. You may well be better than me at this sort of thing - I know almost nothing about combination-stuff. This is a rough guess at a patter that I think exists

[KrazyHorse]

Originally posted by Jaguar
I have never solved a problem like this one

What the **** did you just say to me?

Goddamnit, neither had I until I saw it about 2 days ago.

Mathematics is not about applying known methods. Exercise your goddamn creativity. If you can't do that then you will never progress beyond mere rote ability.

And the people who write those math competitions are creative enough in coming up with problems that you will never be able to excell via knowledge of methods...

[Kuciwalker]

Originally posted by molly bloom

http://www.cals.ncsu.edu/agexed/aee501/aristotle.html

'All students were assigned tasks involving historical or scientific research. Aristotle based many of his scientific propositions upon this research.'

http://www.edst.purdue.edu/georgeoff/EDFA_200/Aristotle.htm

'Although study at the Lyceum seems to have concentrated on rhetoric and logic, a shift shortly was made to the natural sciences, resulting in a curriculum distinctly different from Plato’s Academy.'

Including but not limited to, zoology, marine biology, cosmology, taxonomy, Aristotelean (non-mathematical) logic....

http://people.bu.edu/wwildman/WeirdWildWeb/courses/wphil/lectures/wphil_theme03.htm

'Aristotle’s Lyceum

Founded in 335, close to Athens, when Aristotle was 49
Curriculum emphasized natural science; contrast with Academy’s stress on mathematics, and speculative and political philosophy. '

Sorry, I got the two mixed up. I'm not an enyclopedia

[KrazyHorse]

Originally posted by Kuciwalker
20101?

Thanks, jag. You may well be better than me at this sort of thing - I know almost nothing about combination-stuff. This is a rough guess at a patter that I think exists

Closer. You're off by just under a factor of two.

Where does the number 20101 come from (i.e. what numbers did you multiply together to get that)?

If you tell me I may be able to reverse engineer your mistake

[Kuciwalker]

Originally posted by KrazyHorse
Hint: the prime factorisation of 2004^100 is:

2^200 * 3^100 * 167^100

It's easier if you just think of it as 2x2x3x5 (^100) though - the answer is the same whether you use 5 or 167, and 5 is easier to write

[molly bloom]

Originally posted by Kuciwalker


Sorry, I got the two mixed up. I'm not an enyclopedia

Neither am I.

[Kuciwalker]

Originally posted by KrazyHorse


Closer. You're off by just under a factor of two.

Where does the number 20101 come from (i.e. what numbers did you multiply together to get that)?

If you tell me I may be able to reverse engineer your mistake

200+199+198...+1 (and then tacked on an extra 1 for (3^100)*(5^100))

[Kuciwalker]

Originally posted by molly bloom
Neither am I.

So you just copy and paste from, say, Grolier?

[KrazyHorse]

Obviously.

The really important part is that one of them is to the two hundred whereas the others are to the one hundred....

[KrazyHorse]

Originally posted by Kuciwalker


200+199+198...+1 (and then tacked on an extra 1 for (3^100)*(5^100))

Look more carefully at the pattern that you've built

Some of those numbers are dividing each other...

In fact, if you've built it according to how I think you did, an awful lot of them are...

[KrazyHorse]

The question can be though of as follows:

assign A a number from 0 to 200, B a number from 0 to 100 and C the same

Do it many times in such a way that between any two assignments neither is larger (or equal) in all three categories

Build starting with C = 0

Obviously every other C will be larger, so we need to make either A or B bigger than it will be with any assignement. The way to do this is to start with B at 0. Now it is best to take A = 200 Make every possible combination such that A + B = 200 and you'll be safe so far

There are 101 of these (200,0 199,1 etc)

Now raise C to 1 and find every possible combination st A+B = 199 (101 of these)

Keep going until C = 100

So the answer is 101*101 = 10201

In other words, you found every possible combination such that A + B + C = 200

As an additional exercise, extend this thought to an arbitrary prime factorisation...

[KrazyHorse]

The proof that this is the largest possible applicable subset is substantially more involved. It took me about an hour to see it. My proof is rather involved. There might be a shorter one, but I haven't found it yet...

[Kuciwalker]

Spoiler:

10202?

[molly bloom]

Originally posted by Kuciwalker


So you just copy and paste from, say, Grolier?

No, I strive for accuracy.