[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 349

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Wow! Andrei, and you did all this in your mind?
 
I confess, a little on paper :)
 
In a round-robin chess tournament each participant has played each game once. Call a game wrong if the chess player who won it ended up with less points than the loser. (A win gives 1 point, a draw gives 1/2, a loss 0.)
Can wrong games constitute
a) more than 75% of the total number of games in the tournament;
b) more than 70% ?
 
Pardon me, I'll give you one more problem, OK?
How many total variants of ZZ can be "drawn" on n number of bars, if the tops can only be on Hight and Low bars?
 
joo >>:
Пардон, я ещё до кучи задачку дам, ок?
Сколько всего вариантов ZZ можно "нарисовать" на n-ном количестве баров, если вершины могут быть только на Hight и Low баров?

This one. Give me a more specific task. Does one line count as a zigzag? How about two? What are the "rules of the game" at the ends of a series of bars?

 
MetaDriver >>:

Эта. Задачку поставь поопределённее. Одна линия может считаться зигзагом? А две? А на концах серии баров какие "правила игры"?

The rules of the game - no rules. The minimum allowed number of knees is 2, i.e. one bar. The maximum is equal to the number of bars.

 
Well, yes, you also have to take into account the price movement itself. I don't see how to solve it analytically. Or even numerically.
 
Mathemat >>:
Ну да, тут надо учитывать еще и само движение цены. Я не вижу, как ее решить аналитически. Или даже численно.

There is, however, no price consideration requirement in the problem. The curvature can be anything. The question is how many variants of this curvature there can be.

I'm wondering if it's 2^n by any chance?

 
joo >>:
зы я вот думаю, а не 2^n случайно?

More, and by a lot. At first I thought that too (2^n - 2 to be exact), but then I discovered a lot of unaccounted variations.

 
MetaDriver >>:

....... но потом обнаружил ещё кучу неучтённых вариантов.

Yeah, that's why I turned to the thinkers. there are a lot of two-top options out there, not to mention combinations of haves and lowes.

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