HeroesWorld
  • Log in
  • Create account
  • Mode
    Interface scale

    Loads video thumbnails from YouTube, which lets it see your IP address. Off until you turn it on, and remembered in this browser only.

    Recolours text in posts that would be hard to read on this theme. Off by default, so posts look exactly as their authors wrote them.

Quiz

Everything about everything.
5.0 (1 rating)
User Avatar
Offline Hermit
Registered:
Posts: 3,467
#944
Auto-translated

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!
1
⚖️
0
In reply to Hermit
User Avatar
Online now Злобный Ящур
Registered:
Posts: 9,473
#945
Auto-translated
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).

0
⚖️
0
In reply to Злобный Ящур
User Avatar
Offline Hermit
Registered:
Posts: 3,467
#946
Auto-translated
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!
0
⚖️
0
In reply to Hermit
User Avatar
Online now Злобный Ящур
Registered:
Posts: 9,473
#947
Auto-translated
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).

1
⚖️
0
User Avatar
Offline Hermit
Registered:
Posts: 3,467
#948
Auto-translated
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!
0
⚖️
0
User Avatar
Offline Uranium235
Registered:
Posts: 913
#949
Auto-translated
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.
1
⚖️
0
User Avatar
Offline Hermit
Registered:
Posts: 3,467
#950
Auto-translated

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!
0
⚖️
0
User Avatar
Offline Драккошка
Registered:
Posts: 32,021
#951
Auto-translated
It won't work (because I tried and it didn't).
Same issue.
А, вот почему.

🏹🎪+⛓️♿=💕
0
⚖️
0
In reply to Uranium235
User Avatar
Online now Злобный Ящур
Registered:
Posts: 9,473
#952
Auto-translated
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).

0
⚖️
0
User Avatar
Offline Hermit
Registered:
Posts: 3,467
#954
Auto-translated
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!
0
⚖️
0
User Avatar
Online now Злобный Ящур
Registered:
Posts: 9,473
#955
Auto-translated
55 mm.

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

0
⚖️
0
User Avatar
Offline Hermit
Registered:
Posts: 3,467
#956
Auto-translated
Yes, but explain why.
Всё не так плохо как Вы думаете. Всё намного хуже!
0
⚖️
0
User Avatar
Online now Злобный Ящур
Registered:
Posts: 9,473
#957
Auto-translated
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).

1
⚖️
1
In reply to Злобный Ящур
User Avatar
Offline Hermit
Registered:
Posts: 3,467
#958
Auto-translated
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!
0
⚖️
0
User Avatar
Online now Злобный Ящур
Registered:
Posts: 9,473
#959
Auto-translated
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).

0
⚖️
1