[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 80
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надо в одной точкеI don't think that's going to work. It doesn't say that everything is at right angles.
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.
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.
Hint: Each such line divides the square into two trapezoids, i.e. it intersects its opposite sides.
т.е. пересекает его противоположные стороны.
?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.
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
Да, ошибся. Это входит в условие задачи.
YOPRST