[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 223

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Richie >>:

Я в травах не специалист, я в вашей задаче запутался. Давайте мне ядерный реактор, ну или на худой конец - мультивибратор :)

If the hometown forum says "Give me weed!", then you quit messing with the fucking vibrator and go and study the right subject. And then you're gonna be clear about what you're talking about. Or else you're just gonna... A specialist's not a specialist...

 
Mathemat >>:

Задачка с мехматовского форума, тут.

В той же ветке приведено решение - 12 или 13.

Такой категорический ответ вызывает изумление. Я начал размышлять на досуге и пришел к некоторым заключениям. Но до решения задачи далековато. Кому интересно, присоединяйтесь.

Только прошу не гуглить и не рэмблить, а то станет неинтересно. Наверняка задачка решается элементарно.

0 to 25 What's the big deal?

 
MetaDriver >>: "В головоломке с пастбищем необходимо учесть ежедневный прирост травы. Нам известно, что [...]"

// Я тож решил, тока через жо.. уравнения. Долго пыхтел, блин.

Lloyd's explanation is probably correct, I believe him - but it's a lot of scripts, I couldn't follow it. I solved it another way, also through the ass, but much easier than you (I remember your calculations, in which you slightly failed to integrate).

Let's introduce another beast into the problem, the fourth - Grass. This beast is exotic: it eats a negative amount of itself, as it grows.

The trick is artificial, but it completely equalizes the beasts and the Grass growth factor. I hope you'll check it out :) Now we make a very simple linear equation with this exotic beast in mind (the variable means how much of the pasture each beast eats in a day):


Goat + Goose - Cow = 0 (the very first condition, which I initially neglected)

Goat + Cow + Grass = 1/45

Goose + Cow + Grass = 1/60

Goat + Goose + Grass = 1/90


This system of equations is very easy to solve, without any determinants, by blunt addition or subtraction of the equations.

It turns out that Goat = 1/90, Goose = 1/180, Cow = 1/60, Grass = -1/180. The sum of all is 1/36, like the author's.

 
Mathemat >>:


Вводим в задачу еще одного зверя, четвертого - Траву. Этот зверь экзотический: он жрет отрицательное количество себя же, так как растет.

Уловка искусственная, но она полностью уравнивает зверей и фактор роста травы. Надеюсь, ты ее заценишь :)

Great! Really appreciate these kind of chips. Simple and delicious.

 
Mathemat >>:

Найти все натуральные, каждое из которых является квадратом числа всех своих делителей (10 класс).

P.S. Например, 9. Все делители - это 1, 3, 9, т.е. их три, а 3^2 = 9.

almost broke my head.


A little clarification: the number of divisors of number a is found by assuming that each of the prime factors n_i can occur from 0 to 2*alpha_i times, that is 2*alpha+1 choices for each prime factor in total

 
I'm starting to doubt my own proof... that's about the task at hand
 

Yep, alsu. The answer is the same - 1 and 9. The solution given in the problem book is discouraging in its brevity (three lines). But there logical reasoning of several steps is omitted. If I find it, I'll post it.


Next (grade 10): (239)

Given infinite number sequence {a(n)}. It is known that lim( a(n+1) - a(n)/2; n -> infinity ) = 0. Prove that lim( a(n); n -> infinity ) = 0.

P.P.S. The problem is not complicated, just apply the Cauchy limit definition directly. There is nothing particularly remarkable about it.


And immediately, a new one, which might be of interest not only to the "advanced" (8th grade):



 
Mathemat писал(а) >>


And immediately, a new one, which may be of interest not only to the 'advanced' (8th grade):



but I would venture to guess that 30 glasses, if averaged for a very long time, albeit at random (if the milk doesn't dry out sooner), will equalise the level in the glasses.

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