Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 203
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Next problem.
A trapezium (arbitrary) is given. How using a single ruler (without divisions) divide the bottom base of the trapezoid into 3 equal parts?
The weight is 5.
There are no marks on the ruler and cannot be. The other side of the ruler cannot be used to draw parallel lines.
Well... you haven't said it all.
There is also "reflected in the mirror". You seem to put them in different classes, but I would put them in the same one. In short, it's a matter of taste. You might have to remember geometry and its equivalence transformations.
And if you generalise, then not only modulo 3, but any prime. But that would be a bit much...
The main question is still the first one.
That's easy.
You have to show me...
.
Incidentally, the upper base of the trapezoid is also divided into three equal parts.
zy
But I already see that the solution has already been found.
You could sign the sequence of actions, but I think it's clear as it is.
ss
But I can already see that a solution has been found.
Why are there thoughts? I have the solution, but it takes a long time to describe it... with formulas and vertex coordinates.
You just need to remember the properties of geometric shapes.
(School geometry course 6-7-8 grades)
You just need to remember the properties of geometric shapes.
(School geometry course 6-7-8 grades)
Another one, quite practical.
The terror of the Megamogg village by the damned occupiers continues. This time, having caught Megamogg, the occupiers gave him an ordinary full bottle of water and a carbon ruler, demanding that he count the volume of the bottle, otherwise death. Megamraz examined the bottle carefully: it was not shaped, flat, flat-bottomed, with no label. He performed a few actions and gave an answer. How had he managed it?
Weight - 3.
FAQ:
- What an angle piece is, I hope it's clear to most people. It is a ruler in the shape of a right triangle with divisions on the cathetuses,
- the walls of the bottle are very thin, so you can ignore the volume,
- the bottle comes with an airtight cap (such as a cork),
- at first, the bottle is filled to the brim with water. The water can be poured out, but the poured out water cannot be used again,
- the neck of the bottle may have an arbitrary, very nasty shape - for example, this (this is my drawing of the whole bottle in my own solution of the problem):
If you use a ruler with divisions, you don't need a right angle - you can calculate it anyway.
Yes, it's not hard to calculate with divisions, but only if you express the volume in cubic diameters of the bottom )
ZZZ: But in the trapezoidal problem, the ruler could only connect two points.)
Easy.
All right, you've got me, here's a little harder:
Prove that the ratio AB / CB = 5
In other words, that point C cuts off exactly one fifth of the segment AB.
// If you're really clever, work out an algorithm for dividing the base of a trapezoid into an arbitrary number of equal parts using a "ruler without divisions".
--
Those who wish may join the clever club. ;)