[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 361

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Prival писал(а) >>

Programmers are being recruited.

How would Americans know about worms in libraries? No, it's our task, it's Russian :)

 
Prival >>:

нет не так. правильный ответ содержит слово если. Програмистов же набирают
1. если нумерация томов слева на право то прогрыз 2 обложки + 1 страницу (условие от и до)
2. если нумерация наоборот то 44 мм - 1 стр

No, Sergei, this one is not from Melkosoft, but from a problem book for children from 5 to 15. Why would kids want to go into such a mess? And the addition of a couple of pages - it's a tenth of a millimeter, as a credit does not go.

By the way, about the old ladies - also from the same problem book for kids. Somehow it should be solved in a simpler way.

 
the distance travelled before the meeting
L1=V1*t
L2=V2*t

L2=V1*4
L1=V2*9
equate L1
V1*t=V2*9

for L2
V2*t=V1*4


substitution result t^2=36 answer 6 am
 
Let's keep it even simpler, to make it like babies. The paths the grandmothers took before the meeting are treated as their speed. Suppose the fast one is x>1 times faster than the slow one.
But now the fast one has x times less distance to walk after the meeting than the slow one. Since it also walks x times faster, it will spend x times less time. So x^2 = 9/4, i.e. x = 3/2.
The distance that the slow one will take 9 hours to cover, the fast one has already walked x times faster, i.e. it took it 9/x = 6 hours.
That's it. It took 6 hours to get to 12 from dawn, and dawn came at 12-6 = 6 am.
P.S. We are left with a problem about rams and brothers.
 
Mathemat писал(а) >>
Two brothers had a flock of rams. They sold it and got as many roubles for each sheep as there were heads in the flock. The proceeds were split in half. The older brother got a tenner, the younger one a tenner and so on several times. Then the older brother took his tenner and the younger one ran out of a few rubles. Then the older one took a knife out of his pocket and gave it to his brother as compensation for the missing amount.
The question is, how much is the knife worth?
Less than 10 roubles. Rather less than 9 roubles.
 
And here's more, purely for humour. The highlights are mine.

Here are the problems sent to us by xxxx.

He claims that they are taken from the maths textbook published by EXMO-Press in 2002.
He also notes that the text is NOT changed, but exactly reprinted from the book.

1. A table has had one corner sawed off. How many corners does it have now? And how many corners will it have if you saw off two, three, four corners?
2. There were three carrots and four apples in the plate. How many fruits were in the plate?
3. There were five bulbs burning in the chandelier. Two of them went out. How many bulbs are left in the chandelier?
4. Mummy has a daughter called Dasha, a son called Sasha, a dog called Buddy and a cat called Fluffy.How many children does Mummy have?
5. There are 8 clogs standing in the hallway. How many children are playing in the room?
6. Several tables have 12 legs. How many tables are there in the room?
7. Murka the cat has puppies: one black and two white. How many puppies does Murka have?
8. The two ground squirrels, two swifts and two ground bugs flew in. How many birds are there near my house?
9. Three sparrows sat on the water. One flew away. How many are left?
10. A multicoloured wheel rolls around the table: one corner is red, the other green, and the third yellow. When the wheel reaches the edge of the table, what colour will be visible?
11. There were children's books on the shelf. A dog ran up, took one book, then another, then two more. How many books will she read?
12. Mother dropped a tray, on which there were two cups with flowers, two with peas and berries. How many cups are there now?
13. There are three branches on the oak tree, and on each branch there are three apples. How many apples in all?
14. How many chickens did the rooster hatch if he laid 5 eggs?
15. One banana falls from the tree every 5 minutes. How many will fall in one hour?
16. A rooster and a hen were walking around the yard. The rooster has 2 legs and the chicken has 4 legs. How many legs were walking around the yard?
17. There were five glasses of berries on the table. Misha ate one and put it on the table. How many glasses are there on the table?
18. Three cherries and two apples were embroidered on Masha's dress. One cherry and two apples were eaten. How much fruit was left?

 
Mathemat писал(а) >>
And here's more, purely for humour. The highlights are mine.
Do you know how educators feel about such tasks being given to children? Some of them are positive, some of them are negative :)
I like the first one better, the one about the snake :)
 
OK, bananas on the tree or apples on the oak tree, you don't have to worry about that. But there are some blatantly meaningless problems - 3, 4, 8, for example. The answers depend on how you take them - as a joke or seriously.
All right, you can make a joke, but not to the detriment of the context.
 
An enigma. My composition.
3 heads. 2 legs. 1 tail. What is it ?
1 head. 2 arms. 6 legs. 1 tail. What is it?
My children know the answer ))
 
Nah, that's not how you train your brain, that's how you blow it out of proportion. Well, maybe something like a three-headed two-legged one-tail...
P.S. I forgot about one more problem:
All points of the plane are coloured red or white. Prove that there are at least two points of the same colour, the distance between which is 1 cm.
For some reason no one suggested anything.
P.P.S. The first one (3 heads. 2 legs. 1 tail) is a dragon from fairy tales, I guess.
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