[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 174

 

Richie, hello, have you got the glasses ready?

x is right, y is bottom up. Then x - y after each move equals 2 modulo 4.

 
Mathemat >>:

Следующая. Гулять так гулять (несколько последних задач - из темы инвариантов).

На столе стоят 16 стаканов. Из них 15 стаканов стоят правильно, а один перевернут донышком вверх. Разрешается одновременно переворачивать любые четыре стакана. Можно ли, повторяя эту операцию, поставить все стаканы правильно?

a question for you to ask: how is it "right"? Answer options: a) bottom up, b) bottom down and c) full:)))

 
Mathemat писал(а) >>

Next. A walk is a walk (the last few problems are from the theme of invariants).

There are 16 glasses on the table. Fifteen of them are standing correctly and one is upside down. It is allowed to turn any four glasses upside down simultaneously. Is it possible, repeating this operation, to put all the glasses correctly?

Never :) 15 correctly is not divisible by four.

 

https://c.mql5.com/mql4/forum/2009/11/DC.rar

https://www.mql5.com/ru/forum/122181/page17

It's just to kill the theme with turns. After this shit, this kind of thing looks pretty lame. ;)

The first archive contains the programme. The second link is to the "user manual" (in the forum text).

2 Mathemat: You don't have to download it, I sent it to you by email once. Go to your email account and save your bandwidth. :)

.

 

https://www.mql5.com/ru/forum/122181/page17
Uh, I'd say all I think about Norbekov, but this is not the right forum, I'll say nothing :)

 

OK, enough of the elementary stuff. Make it more complicated:

Construct a right triangle, one vertex of which lies at the given point, the second on the given line, and the third on the given circle.

 
Richie >>:

https://www.mql5.com/ru/forum/122181/page17
Ух сказал бы я всё, что думаю про гражданина Норбекова, да не тот это форум, промолчу :)

Yeah, sure. Better get through some levels with compasses. Then you can report back on how many you've passed.

// I'll take your word for it.

 
Mathemat >>:

Ладно, хватит элементарщины. Посложнее:

Постройте правильный треугольник, одна вершина которого лежит в данной точке, вторая на данной прямой, а третья на данной окружности.

Yeah. Sounds like fun. I thought it was a joke at first, but then I discovered the word "correct" and the joke immediately ended ;)

 
Mathemat >>:

Ладно, хватит элементарщины. Посложнее:

Постройте правильный треугольник, одна вершина которого лежит в данной точке, вторая на данной прямой, а третья на данной окружности.

Which is the right one?

You don't have to answer that. I looked it up on wikipedia... very surprised :)

 

Here:

Reason: