[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 80

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Mischek >>:


надо в одной точке

I don't think that's going to work. It doesn't say that everything is at right angles.

 
vegetate >>:

что-то мне кажется невыйдет. Там-же не написано, что все под прямыми углами.


Probably need to draw, but at a guess there are probably 8 that will meet the conditions and start in pairs of 8 dots

the ninth is doomed to overlap with any of the eight.

But it's not certain.

I have to draw and count.

 
vegetate >>:

что-то мне кажется невыйдет. Там-же не написано, что все под прямыми углами.


Actually, yes.

Then, at a glance, you can get by without crossing the three at one point

I won't draw it now.

 
Man, that's a fun task.
 

Hint: Each such line divides the square into two trapezoids, i.e. it intersects its opposite sides.

 
Mathemat >>:

т.е. пересекает его противоположные стороны.


?
 
Mathemat >>:

Подсказка: каждая такая прямая делит квадрат на две трапеции, т.е. пересекает его противоположные стороны.

Is that a hint, or is it a condition? You can also draw such a line through adjacent sides.

 

Yes, my mistake. This is part of the condition of the problem.

 
vegetate >>:



And if you come at it from the other side

We choose a point in the square

draw two lines intersecting in this point, respecting the 2/3 rule

The question is whether it is possible to draw a third line through this point, respecting the 2/3 rule

at a glance - no

 
Mathemat >>:

Да, ошибся. Это входит в условие задачи.


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