[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 580

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sand: I will think about it.

I also sent a version I had written an hour ago to be checked.

If, however, the car on which the counter is reset turns out to be the first in the second counter, then the 4-2 scheme changes to 3-1.

 
There seems to be no way around it without going back to the starting point. We need to minimise the number of returns.
 
GaryKa:
It's a difficult scheme, you have to move in.
 

A great resource, by the way, this braingames.ru.

Все решает время. Вы потерпели кораблекрушение и попали в плен к племени каннибалов. Вам в руки дают пару песочных часов: одни отсчитывают ровно 4 минуты, другие — ровно 7. Вождь требует, чтобы вы сказали, когда пройдет точно 9 минут. Если вы это сделаете, вас освободят. Если вы не сделаете этого, вас съедят. Вождь орет: «Начинай отсчитывать немедленно, никакой подготовки!» Что делать?

 
Mathemat:
I don't know exactly how, but 7+(4/2)=9. Maybe put a four-minute clock on your finger - it would be like a scale.
 

4 + 3 + 1 + 1.

The first thing to do is to put all the clocks running and think, and think :))

 
Two mega-brains have a layered (i.e. you can't cut horizontally) rectangular cake, from which some creep has unfortunately already cut (and eaten) a rectangular piece. The orientation and position of the cut piece can be completely arbitrary. How do you divide the remaining cake into two equal-sized pieces with one straight cut?
 
Mathemat:
Two mega-brains have a layered (i.e. you can't cut horizontally) rectangular cake, from which some creep has unfortunately already cut (and eaten) a rectangular piece. The orientation and position of the cut piece can be completely arbitrary. How do you divide the remaining cake into two equal-sized pieces with a single rectilinear cut?
Mark the intersection point of the cake diagonals and the intersection point of the cut-out diagonals. Make the cut by passing through both points in a straight line.
 
alsu:
Mark the intersection point of the cake diagonals and the intersection point of the cut-out diagonals. Make the cut with the line passing through both points.
Why " two mega-brains"?)
 
alsu:
Mark the intersection point of the cake diagonals and the intersection point of the cut-out diagonals. Make the cut with the line passing through both points.

... When these points match, cut the cake as if there were no cut :)
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