[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 158
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Эмм Вы аналитического хотите что ли? Вряд ли дождетесь.
Well, it was supposed to be in the magazine somehow. You can't go through 40 million-plus options in '95.
If one can arrange such a structure from a tetrahedron, why can't one from a cube
No and that's it! Because if you could, the forex distribution would be normal or at least strictly Cauchy. It's a hybrid with bifurcation manners.
By the way, a cube is a tetrahedron with a triangular pyramid on each face. And a triangular pyramid differs from a tetrahedron only in proportions of the sides, but precisely also has 4 sides and 6 edges. Thus both a tetrahedron and a triangular pyramid are murahedrons.
If we put a cube together from a tetrahedron and 4 pyramids, the edges of the tetrahedron will be diagonals of the faces of the cube. And along these diagonals 1 edge of the tetrahedron and 2 edges of the adjacent pyramids coincide. A new problem arises.
Take 1 natural murahedron and 1 murahedron with doubled numbers along the edges. From these two objects, using as many as is necessary, fold the cube so that the ants do not walk along the diagonals. That is, the total number of ants on the edges of the tetrahedron and coinciding edges of the pyramids should be equal to zero. At that, of course, it is desirable to keep the former condition - all numbers on the edges of the cube are different.
I'm not sure that the formulation of the problem is correct - I made it up myself. :-)
But if it's correct or can be made correct, then its solution is also a solution of Sanyooook's problem.
There may be an analytical one, but it is unlikely to cover all solutions. It's not like such a task was set. It would be better to find one, and there are already several.
sanyooooook, have you found many solutions - or have you been looking for at least one solution for 3 years?
а кто-то возмущался что решения нет
Firstly, "someone" was not outraged, but expressed an opinion. Initial formulation of the problem was quite confusing - numbering was not connected with any criteria,
so it seemed that it was proposed to make a single closed route for ants passing through all vertices and edges. Such a route could not be made,
Which "someone" declared and was right. However it turned out that the problem had been originally misunderstood.
// Which is not surprising. :) It's good that yesterday Alexey (Matemat) got something intelligible out of someone. :)
After that "someone" solved it for the tetrahedron, and all evening persistently and successfully progressed in solving it for the cube. Due to difficulty of manual solution I had some doubts about solvability,
However, after finding the correct odd-odd arrangement, the doubts diminished. In the evening maybe "someone" will find a couple more solutions (did I do it for nothing?). =))
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zy. Does it really have 24 unique (not dependent on rotations) solutions? How do you know?
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зы. У неё действительно 24 уникальных (не зависящих от поворотов) решения? Откуда известно?
I'm wondering the same thing.By the way, if we take a murahedron and add it to a murahedron rotated arbitrarily, we obtain a murahedron again! But with other numbers on the edges. (It is supposed that a murahedron is a closed graph-tetrahedron where numbers on its edges need not be all different).
Nevertheless the set of murahedrons does not form a group since it has no unit element.
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зы. У неё действительно 24 уникальных (не зависящих от поворотов) решения? Откуда известно?
From the same list. The given one was just the first one. About the turns - I'm absolutely not sure. We were looking for combinations in which
1. The condition (sum of the numbers of the two sides equals the third number) is satisfied at each vertex.
2. The numbers of the sides are not repeated.
If no one wants to look analytically - I can put the whole list, you can try for turns.
Из того-же списка. Приведенный был просто первым. Про повороты - я абсолютно не уверен. Искались комбинации при которых
1. в каждой вершине удовлетворяется условие (сумма чисел двух сторон равна третьему числу).
2. числа сторон не повторяются.
Если искать аналитически желания ни у кого не осталось - могу весь список выставить, можно будет попроверять на повороты.
Come on
ДавайLet's wait a little longer. MetaDriver wanted a couple of solutions, why ruin a man's buzz :).