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Offline Hermit
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#944
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Let's correlate the rectangles and the space around the graph's vertices. If it's possible to get from one rectangle to another, then they are connected by an edge. Since vertices B and D have odd degrees, it's impossible to construct an Eulerian cycle!
Всё не так плохо как Вы думаете. Всё намного хуже!
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Online now Злобный Ящур
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#945
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Hermit

Let's correlate the rectangles and the space around the graph's vertices. If you can get from one rectangle to another, they are connected by an edge. Since vertices B and D have odd degrees, it is impossible to construct an Eulerian cycle!
A cycle isn't necessary. It's not required to end where you started! And the diagram is incorrect...

Ничто не возникает из ничего и ничто не пропадает бесследно.
Если где-то чего-то убудет, то в другом месте добавится.
(Закон сохранения).

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Offline Hermit
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#946
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Evil Lizard
A cycle isn't necessary. It's not required to end where you started!
And vertex C also has an odd degree!
That's true, but there should still be a situation where a single edge would create an Eulerian cycle, but since we have 3 vertices with odd degrees, even if we connect two of them with an edge, one will still have an odd degree. This proves that it's impossible!!!

Added 4 minutes later
That is, even if we start in rectangle B and end in rectangle D (or vice versa) (connect them with an edge), since 5 edges lead to vertex C, we will still have to traverse one of them twice or not at all. This proves the theorem about the Eulerian cycle.
Всё не так плохо как Вы думаете. Всё намного хуже!
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Online now Злобный Ящур
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#947
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Hermit
because we have 3 vertices with odd degrees
Actually, there are 4: A, C, E, F, since A is connected to B, D, E, and F by two curves. Everything else is correct; there should be no more than 2 vertices with odd degrees. Guess.

P.S. A fellow traveler from St. Petersburg to Moscow once proposed this problem. It was like a bet: if you draw it before we arrive, I'll pay you $100; if not, you pay me. Hermit, was that you by any chance?:D I refused, of course...

Ничто не возникает из ничего и ничто не пропадает бесследно.
Если где-то чего-то убудет, то в другом месте добавится.
(Закон сохранения).

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Offline Hermit
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#948
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No. I encountered it myself, and I believe it was the first time.

Added 1 minute later
I understand about the two curves. Exactly!
Всё не так плохо как Вы думаете. Всё намного хуже!
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Offline Uranium235
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#949
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It won't work (because I tried and it didn't).
There are 3 rectangles inside, each with 5 segments. There are no problems with the two upper right and upper left ones; 2 entrances - 2 exits.
But where there are 5 sides, the line must either enter twice and exit three times, or enter three times and exit twice. For two of them, the problem can be solved because we have free ends of the line (so we can start inside one and end inside another), but the line cannot pass through the third rectangle with 5 segments. (that is, it enters and exits, enters and exits, and for the fifth side, it needs to enter and stay there).

I'm slow.
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Offline Hermit
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#950
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Degree A - 9.
Degree B - 4.
Degree C - 5.
Degree D - 4.
Degree E - 5.
Degree F - 5.

Total - 4 vertices with odd degrees!

Added 7 minutes later
Now there's nothing to guess. Let someone else guess, for example, Uranium. He also solved it and even did it before me.
Всё не так плохо как Вы думаете. Всё намного хуже!
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Offline Драккошка
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#951
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It won't work (because I tried and it didn't).
Same issue.
А, вот почему.

🏹🎪+⛓️♿=💕
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#952
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Uranium235
I tried, but it didn't work.
Драккошка
Same here.
Let's all chip in 100 bucks!!!:D

Ничто не возникает из ничего и ничто не пропадает бесследно.
Если где-то чего-то убудет, то в другом месте добавится.
(Закон сохранения).

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Offline Hermit
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#954
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Let me make a guess first.
Attachments 1
1 file attached • Total size: 20.0 KB
Всё не так плохо как Вы думаете. Всё намного хуже!
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Online now Злобный Ящур
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#955
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55 mm.

Ничто не возникает из ничего и ничто не пропадает бесследно.
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Offline Hermit
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#956
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Yes, but explain why.
Всё не так плохо как Вы думаете. Всё намного хуже!
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#957
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8 ml was used, i.e., 8000 cubic mm – which is exactly the volume of a cube. Therefore, the side of the cube = 2 cm, which corresponds to 4 divisions on the beaker. Therefore, 1 division = 5 mm.

Ничто не возникает из ничего и ничто не пропадает бесследно.
Если где-то чего-то убудет, то в другом месте добавится.
(Закон сохранения).

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Offline Hermit
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#958
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Evil Lizard
It took 8 ml, i.e., 8000 cubic mm – exactly the volume of a cube. Therefore, the side of the cube = 2 cm, which corresponds to 4 divisions on the glass. Therefore, 1 division = 5 mm.
Now, make a wish.
Всё не так плохо как Вы думаете. Всё намного хуже!
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Online now Злобный Ящур
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#959
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There is a land plot in the shape of a convex 111-sided polygon. Its owner wants to divide it into smaller plots in the shape of parallelograms for subsequent sale. What are his chances of success in this endeavor? Naturally, not a single piece of land should be wasted!

Ничто не возникает из ничего и ничто не пропадает бесследно.
Если где-то чего-то убудет, то в другом месте добавится.
(Закон сохранения).

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