[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 296

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Mathemat писал(а) >>

Environmentalists have protested against the high volume of logging. The chairman of the timber company reassured them as follows: "There are 99 per cent of pine trees in the forest. Only pines will be cut down, and the percentage of pines will remain almost the same - 98 percent. What part of the forest has been earmarked for felling?

Mathemat, well finally they started posting problems that I can soberly solve :)))
Yes, cunning chairman and stupid environmentalists :)))
 
And the first one, Richie?

Three runners A, B, C ran the 100 metre race several times. When the results were tallied, it turned out that A beat B in more than half of the races, B beat C in more than half of the races, and C beat A in more than half of the races. Could this happen? (from the Steingauz problem book)
 
Yeah, count the number of divisors for now. So far, I don't think your conclusion is justified or potentially useful.
All we know about the runners is what the problem says. Probably all three of them.
 

I have written a program to calculate the number of divisors:
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Dim koldelitVsego As Long
Dim koldelitChisla As Long
Dim i As Long
Dim ii As Long
-

Private Sub Command1_Click()
koldelitVsego = 0
For i = 1 To 2002
koldelitChisla = 0
For ii = 1 To i
If ((i / ii) - Int(i / ii)) = 0 Then koldelitChisla = koldelitChisla + 1 'If = 0 then divide
Next ii
 koldelitVsego = koldelitVsego + koldelitChisla
'Print i, koldelitChisla
 Next i
Print koldelitVsego
End Sub
-
It turns out 15542 pieces

 
OK. Now let's think about what we get. If the first one crossed out 100 = 2^2*5^2 with all divisors (1, 2, 4, 5, 10, 20, 25, 50, 100), then the second one, when crossing out 15 with divisors, can't cross out 1 and 5, because they are already gone. What is the purpose of this program then?
 
On a neighbouring thread, Perelman, who is Yakov, was remembered. He had some books, too:
"For Young Mathematicians. The First Hundred Puzzles" and "The Second."
Maybe something from there will come in handy.
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I came across this movie: Fermat's Trap.
There's four mathematicians locked in a room, forced to solve these logical-mathematical problems under the threat of physical destruction. If you don't, death's coming. Brrrrrr.
It's actually a detective story. Specific.
Anyone seen it? It's very similar to this one. You're doing riddles, too. No self-mutilation here, though.
 
Svinozavr >>:
Очень похоже на эту ветку. Тоже загадки отгадываете. Правда, здесь без членовредительства.

Ahem... Why do you think there are fewer people left in the branch than there were in the beginning...?

 
MetaDriver >>:

Гхм.. А как ты думаешь, почему в ветке осталось меньше народу чем было вначале...?

I haven't gone anywhere, I just don't have time for forums now :)))

 
alsu >>:

я кстати никуда не ушел, просто щас времени на форумы нет:)))

Where do you get off the submarine... and as for time, there isn't any. :))

 
I thought that Perelman was not only promoting physics to the masses, but also mathematics.
Svinozavr, what do you say about runners?
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