How many great-grandparents do all of his great-grandmothers have. From the family archive - great-great-grandfather and great-great-grandmother Pantel. Find the area of the pan
Each person has 2 parents, 4 grandparents, 8 great-grandparents.
281. Dialogue in a household goods store:
How much does one cost?
20 rubles, - the seller answered.
How much is 12?
40 rubles.
Okay give me 120.
Please, 60 rubles from you.
What did the visitor buy?
Room for an apartment.
A bottle with a cork costs 1 p. 10 k. A bottle is more expensive than a cork by 1 p. How much is the bottle and how much is the cork?
At first glance, it may seem that a bottle costs 1 ruble, and a cork 10 kopecks, but then a bottle is 90 kopecks more expensive than a cork, and not 1 ruble, as by convention. In fact, a bottle costs 1 r. 05 k., and the cork costs 5 k.
Katya lives on the fourth floor, and Olya lives on the second. Rising to the fourth floor, Katya overcomes 60 steps. How many steps does Olya need to climb to get to the second floor?
At first glance, it may seem that Olya walks 30 steps - half as many as Katya, since she lives two times lower than her. Actually it is not. When Katya goes up to the fourth floor, she overcomes 3 flights of stairs between floors. So there are 20 steps between two floors: 60: 3 = 20. Olya climbs from the first floor to the second, therefore, she overcomes 20 steps.
How to pour exactly half of a mug, ladle, pan and any other dishes of the correct cylindrical shape, filled to the brim with water, without using any measuring instruments?
Any dish of the correct cylindrical shape, when viewed from the side, is a rectangle. As you know, the diagonal of a rectangle divides it into two equal parts. Similarly, a cylinder is bisected by an ellipse. It is necessary to drain water from a cylindrical dish filled with water until the surface of the water on one side reaches the corner of the dish, where its bottom meets the wall, and on the other side, the edge of the dish through which it is poured. In this case, exactly half of the water will remain in the dishes:
Three hens lay three eggs in three days. How many eggs will 12 hens lay in 12 days?
You can immediately answer that 12 hens will lay 12 eggs in 12 days. However, it is not. If three hens lay three eggs in three days, then one hen lays one egg in the same three days. Therefore, in 12 days she will lay: 12: 3 = 4 eggs. If there are 12 hens, then in 12 days they will lay: 12 4 = 48 eggs.
Name two numbers in which the number of digits is equal to the number of letters that make up the name of each of these numbers.
One hundred (100) and one million (1000000)
I vouch, - said the seller in the pet store, - that this parrot will repeat any word it hears. A delighted buyer bought a miracle bird, but when he came home, he found that the parrot was as mute as a fish. However, the seller did not lie. How is this possible? (The task is a joke.)
The parrot can indeed repeat every word it hears, but it is deaf and does not hear a single word.
There is a candle and a kerosene lamp in the room. What will you light first when you enter this room in the evening?
Of course, a match, because without it you cannot light a candle or a kerosene lamp. The question of the task is ambiguous, because it can be understood either as a choice between a candle and a kerosene lamp, or as a sequence in lighting something (first a match, then - from it - everything else).
Half of half a number is equal to half. What is this number?
This number is 2. Half of this number is 1, and half of half of this number (i.e. one) is equal to 0.5, i.e. also half.
Over time, a person will definitely visit Mars. Sasha Ivanov is a man. Consequently, Sasha Ivanov will eventually visit Mars. Is this reasoning correct? If not, what is wrong with it?
The reasoning is wrong. It is not necessary that Sasha Ivanov eventually visit Mars. The external correctness of this reasoning is created due to the use of one word (“man”) in it in two different senses: in the broad (abstract representative of humanity) and in the narrow (concrete, given, this particular person).
It is often said that one must be born a composer, or an artist, or a writer, or a scientist. Is this true? Is it really necessary to be born as a composer (artist, writer, scientist)? (The task is a joke.)
Of course, a composer, as well as an artist, writer or scientist, must be born, because if a person is not born, then he will not be able to compose music, draw pictures, write novels or make scientific discoveries. This joke problem is based on the ambiguity of the question: "Do you really have to be born?" This question can be understood literally: is it necessary to be born in order to engage in any type of activity; and also this question can be understood in a figurative sense: is the talent of a composer (artist, writer, scientist) innate, given by nature, or is it acquired during life by hard work.
You don't have to have eyes to see. We see without the right eye. We also see without the left. And since we have no other eyes besides the left and right eyes, it turns out that neither eye is necessary for vision. Is this statement true? If not, what is wrong with it?
The reasoning is, of course, wrong. Its external correctness is based on the almost imperceptible exclusion of one more option, which in this reasoning also had to be considered. This is an option when not a single eye sees. It was he who was omitted: “Without the right eye we see, without the left too, which means that the eyes are not necessary for vision.” The correct statement should be: “Without the right eye we see, without the left we also see, but without two together we do not see, which means that we see either with one eye, or the other, or both together, but we cannot see without eyes, which, thus necessary for vision."
293. The parrot lived less than 100 years and can only answer yes and no questions. How many questions does he need to ask to find out his age?
At first glance, it may seem that a parrot can be asked up to 99 questions. In fact, you can get by with a much smaller number of questions. Let's ask him like this: "Are you over 50 years old?" If he answers "yes", then his age is from 51 to 99 years; if he answers “no”, then he is from 1 year to 50 years old. The number of options for his age after the first question is halved. The next similar question: “Are you more (you can ask - less) 25 years old?”, “Are you more (less than) 75 years old?” (depending on the answer to the first question) reduces the number of options by four times, etc. As a result, the parrot needs to be asked only 7 questions.
One man who fell into captivity recounts the following: “My dungeon was in the upper part of the castle. After many days of effort, I managed to break one of the bars in the narrow window. It was possible to crawl through the resulting hole, but the distance to the ground was too great to simply jump down. In the corner of the dungeon, I found a rope forgotten by someone. However, it turned out to be too short to be able to go down it. Then I remembered how one wise man lengthened a blanket that was too short for him, cutting off part of it from below and sewing it on top. So I hurried to split the rope in half and re-tie the two resulting parts. Then it became long enough, and I safely went down it. How did the narrator manage to do this?
The narrator divided the rope not across, as it most likely might seem, but along it, making two ropes of the same length out of it. When he tied the two pieces together, the rope became twice as long as it was at first.
How many great-great-grandparents did all your great-great-grandparents and great-great-grandparents have?
ANSWER
Each person has 2 parents, 4 grandparents, 8 great grandparents, 16 great great grandparents. To find out how many great-great-grandmothers and great-great-grandfathers all of the great-great-grandparents of each of us had, we need 16 x 16. It turns out 256. This result is obtained, of course, if we exclude cases of incest, i.e. marriages between different relatives.
If we take into account that one generation is approximately 25 years, then eight generations (which were discussed in the condition of the problem) correspond to 200 years, i.e. 200 years ago, every 256 people on Earth were relatives of each of us. In 400 years, the number of our ancestors will be 256 x 256 = 65,536 people, i.e. 400 years ago, each of us had 65,536 relatives living on the planet. If we “unscrew” history a thousand years ago, it turns out that the entire population of the Earth at that time was relatives of each of us. So, indeed, all people, by and large, are brothers.
I put the family archive in order - I scan photos and interview everyone who remembers what. I'll try to post the results here.
This is the oldest photograph of relatives from my mother's side. Photograph from the late 19th century. On it is my great-great-grandfather Grisha (Gotlib) and great-great-grandmother Anyuta (Ita Aronovna) Pantel.
In our family they were called "grandfather Grisha" and "grandmother Anyuta", so I will call them the same - although they are my great-great-grandfather and great-great-grandmother.
Grandfather Grisha was from Belovezhskaya Pushcha. He was a Nikolaev soldier, demobilized from the army ahead of schedule - due to tuberculosis. And as he served in the Nikolaev army, he received permission to settle outside the Pale of Settlement. So he ended up in the city of Karachev.
Karachev is a small town 44 km from Bryansk, a very old Russian city. Arriving there, grandfather Grisha Pantel married his grandmother Anyuta (Ita Aronovna Livshits).
Grandmother Anyuta, originally from Odessa, was an orphan. She was born in 1871. Her mother died in childbirth when Anyuta's grandmother was very young. And when she was 5 years old, during a pogrom in Odessa, her father died, and she was sent to relatives from her father's side. When she grew up, she studied at a seamstress and hat workshop. She married at the expense of the Jewish community.
Unfortunately, we do not know anything about the family of the great-great-grandfather, grandfather Grisha. His daughter, my great-grandmother Fenya, recalled that once his parents came to them - her grandfather and grandmother. She was then small, the only thing she remembered was that her grandmother was wearing a wig. His older brothers (and he was the youngest in the family) went to America.
He worked all his life as a shoemaker, he had his own workshop, kept 2-3 apprentices. Grandmother Anyuta kept a seamstress workshop and she always had orphan girls in training, well, her daughters helped. They didn't have their own house, they rented it.
They had 17 children, and only seven survived to adult (or at least young) age. Ten died in infancy and childhood.
And seven are Fedor (Fayvel), born in 1898, he died in civilian life, the eldest. The third is Sonya (Sarah), born in 1900, she lived all her life in Bryansk. I already remember her - we came to visit relatives in Bryansk when I was 10 years old, and there I saw my grandmother Sonya. The fourth is my great-grandmother Fenya (Feiga Leya), born in 1902, died in 1985. Then Sergei (Israel), born in 1904, he died a year or two after the revolution - he was shot dead at the post, he was a Red Army soldier. There was also Reuben, born in 1908 (died in the 60s), Efim, born in 1910 (disappeared in the Second World War), and daughter Frida, born in 1912. (she died at the age of 12: she was gored by a bull, she was seriously ill for a long time, was paralyzed and died after some time).
This photograph is about 1912. Grandmother Anyuta has three younger children - Reuben, Efim and little Frida.
Part of the inscription "Karachev city" is visible on the passe-partout below.
The year of this photo is also not signed, so I date it to about 1928. Grandmother Anyuta is sitting in the center.
My great-grandmother Fenya is standing on the left, I think she is 17 years old. To her right is her brother Yefim. The handsome young man sitting on the left is Brother Reuben. Little girls next to grandmother Anyuta - two granddaughters, Sonya's daughters (Fenya and Rosa - behind the barrier).
In 1915, the father's brothers, Grisha's grandfather, sent a code card to Fenya and Sonya - so that they would move to live in America. They were collected on the road, but at the last moment, grandmother Anyuta did not let her daughters go.
Ten of her children, as I wrote, died in childhood and infancy. Several children died literally on the same day - one fell ill with diphtheria. There was never much money in the house, and on the advice (sort of) of neighbors, they put the little ones together - so that everyone would get sick at once, well, so as not to call a paramedic to each separately, because it’s expensive! So they were all buried together.
In matters of raising children, apparently, they did not go far for a belt. My great-grandmother Fenya told me how one day the nanny gave the girls a rag doll for the holiday. There were never too many toys in the house, and the girls reveled in the gift. Well, the boys took away the doll and cut it up - to see what was inside it. As a result, the father whipped everyone with a spear - both the boys - for being taken away and cut up, and the girls - for roaring, and the nanny got it - for bringing the doll.
Grandmother Anyuta observed Jewish traditions. Therefore, for a long time she could not come to terms with the fact that her daughter - my great-grandmother - married a Russian, for many years she did not communicate with her because of this. And when her husband, grandfather Grisha, died in 1921, she went to live not with my great-grandmother with her "Russian husband" Vasily Pervushov, but with her sister Sonya, whose husband was "correct" - Yuda Livshits.
After the war, however, apparently due to the prescription of years, the national question ceased to be so acute, and until her death, grandmother Anyuta lived with my great-grandmother Fenya and her family, nursed her great-granddaughters - my mother and her sister.
She was very accommodating, non-confrontational. Everyone in the house loved her and went to her for advice.
This photograph is from 1950, Lvov. My mother is 7 months old, and her great-grandmother, grandmother Anyuta, who is 79 years old, is holding her in her arms.
My mother remembers the last years of Anyuta's grandmother's life. I also happened to see something - not the grandmother herself, of course, but her prayer book. Old, old Jewish prayer book of the 18th year of publication. I remember him from childhood, he was upstairs in the closet. At first, he did not interest me in any way, but when I began to go to the Jewish school at the synagogue and parse the words in Hebrew, I saw familiar words in my great-great-grandmother's prayer book.
Mom remembers that Anyuta's grandmother always had a prayer book, and not just lay, but was used all the time - she often prayed.
She also went to the synagogue in Lviv, where the whole family moved after the war. Grandmother Anyuta knew how to read prayers in Hebrew, and because she helped other women to pray - she said the words aloud, and they repeated after her - they bought her a place in the synagogue on a bargain.
She told my mother stories from the Torah, and in general she was glad to tell everyone who was ready to listen to her.
In addition to Russian and Hebrew (prayer), she spoke Yiddish well.
Mom remembers that Anyuta's grandmother said blessings for food - she whispered a short prayer before eating anything. Before Pesach, there was matzo in the house - in Lvov they bought local matzo, and when they moved to Krasnodar, there was no matzo bakery and synagogue there, and her daughter Sonya from Bryansk sent matzo for Pesach in a parcel.
She had a very small pension - she received it for her son Yefim, who died in the Second World War. From this pension, she gave birthday gifts to her daughter and granddaughter (my great-grandmother and grandmother) one crystal glass a year - all that she managed to save money for. She bought wine glasses "in the suit", and therefore a set of wine glasses was assembled in a few years :)
When she was already quite old, a TV appeared in the house. And she watched TV shows until late at night, could not turn off the TV - she was afraid that she would offend the television lady with this. My grandfather, my mother's dad, used to say to her: "Anna Efimovna, turn off the TV and go to sleep!" And she always answered: "How can I turn it off when she looks at me and talks!" And only when the TV presenter said goodbye to the audience until tomorrow, Anyuta's grandmother wished her good night and also went to bed :)
Before her death, her hands shook violently, and in order to somehow overcome this, she constantly crocheted. She died in 1962, at the age of 91. She was buried in the Jewish cemetery in Krasnodar. Since there was no Jewish funeral service in Krasnodar in those years, at her request a person familiar with the traditions was found, he accompanied her with her relatives to the last, even if he read Kaddish.
Every person has their roots. Some people are proud of their ancestors. Some people don't know anything about them. Someone has their own genealogical tables for a hundred or two years ago. Some people only know their mom and dad. Those who grew up in an orphanage often do not know about them either.
However, for everyone without exception, both those who know and those who do not know, one can be sure of one and the same circumstance. Each person had these very ancestors. And they were all along the chain, throughout the depths of centuries, to Adam and Eve. Without knowing them by name, we know for sure that they always existed.
And then one day I thought about a very simple thing. And how many of them were there? Asking this question, I firmly knew that there were A LOT of them.
And yet I decided to try to count. Perform purely arithmetic operations and simply find out their total number. Well, at least until Christmas. In just over two thousand years.
The result stunned me.
No, I did not count until the planned time. I couldn't. But even to a more modest historical depth, I got completely crushed by the incredibleness of the calculated.
I am not a mathematician. Therefore, I simply don’t know the names of the orders of numbers following trillions and billions. And ten, to some extent, to me, as again a layman in mathematics, does not say much.
You can define your feelings only in such a word. Space. The same finite infinity.
Naturally, generations should be taken as objects of calculation. Father, mother is the first. Grandparents - the second. Great-grandfathers - the third. Etc. I took the difference between generations of 20 years. Someone can take another number, 25 there or 30 - it doesn't matter. Because the further you count, the more clearly you will understand that this does not affect the order of the numbers at all.
1 generation (father, mother) - 2 people.
2 generation (grandfathers, grandmothers) - 4 people.
3rd generation (great-grandfathers, great-grandmothers) - 8 people.
4th generation (great-great-grandfathers, great-great-grandmothers) - 16 people.
5th generation (we omit the degree of relationship further) - 32 people.
We have reached the end of the 19th century. As you can see, each of us in the twentieth century had 62 ancestors.
I won't count any further. You can take a pencil and do it yourself.
Let me just summarize.
In the 19th century (generations 6 to 10), I (and you) had one thousand nine hundred and eighty-four ancestors. The 10th generation alone gives 1024 ancestors.
I'll tell you right away. Counting, you will definitely notice that every 10 generations (or 200 years by my count) gives an increase in the number of about a thousand times. I didn't make a reservation. Not AT 1000. But 1000 times more.
Here is a direct and first confirmation of this. The 5th generation, as we have just seen, is 32 people. The 15th generation is 32 thousand 768 people.
And in just 15 generations - over 65 thousand people.
Note. This is just 300 years. We have reached only the time of Peter.
Another 200 years, or 10 generations. In total, this will be five hundred years and 25 generations from this day. In total, during this time you had approximately 67 million ancestors. Only your direct ancestors. And you only have one.
In just one thousand years, from the time of Rurik and Svyatoslav (note that the time difference between them is no longer important here) to the present day, each of our contemporaries has one thousand trillion (or a million billion, as you like) ancestors.
But there were centuries before that, about which we know nothing. Times of Goths-Huns, Scythians and Sarmatians. I'm not talking about the Bronze Age, the Paleoliths and so on.
Anyone who wants to can calculate this space with their own hands.
Of course, all these calculations are wrong.
If at the time of Batu (somewhere in the 39th or 40th generation) you have somewhere around 500 or 1000 billion ancestors, this, of course, does not mean that at that time at least 500 or 1000 billion people lived on Earth. And even more so, trillions or billions of people have never lived on our planet at the same time.
Yes, even if we remember that these astronomical numbers are related to just one single person. But there is also humanity.
Humanity, as we see today, is not decreasing in number. On the contrary, it is growing.
During the time of the Roman Empire, if I am not mistaken, only a few million people lived in it. But this is almost all of today's southern, central and western Europe, western Asia and northern Africa.
There are now more than six and a half billion inhabitants on Earth, and their number is growing all the time.
So with the calculation of our ancestors, it turns out that arithmetically everything is perfect here. But in life this cannot be, because it can never be.
The thing is that all these calculations do not take into account one, but a very important factor.
Of course I know him. But I will not voice.
Because it is very important that each person understands this very factor himself. And he also came to the conclusions that follow from this factor.
Checksum - 2014
1. Looking at the family album, Vanechka discovered that he had 4 great-grandmothers and 4
great-grandfathers. And how many great-grandmothers and great-grandfathers had his great-grandmothers and
great-grandparents all together?
Solution:
Each person has 4 great-grandparents and 4 great-grandfathers. Because all great-grandparents
Vanichka had 8, then 8 * 4 \u003d 32 great-grandmothers and 32 great-grandfathers were with the Vanichkins
great-grandparents and great-grandparents combined.
Answer: Vanichka's great-grandmothers and great-grandfathers had 32 great-grandmothers and 32 great-grandfathers combined.
2. Two trains are moving towards each other. Their speeds are 105 km/h and 85 km/h.
How far apart are these trains half an hour before they meet?
105 0.5 + 85 0.5 = 95 Answer: 95 km.
3. Find the value of the expression 12 log 9 27.
Solution: Because =1 and = at x 0 we have:
12 9 27 = 12 9(33) = 12 3 9 3 = 12 3 = 18 Answer: 18.
4. The centers of non-intersecting circles of radius 2 are located at the vertices of the triangle. What is the sum of the areas of the three shaded sectors?
Solution: It is known that the sum of all angles of a triangle is 1800. circles of the same radius, and the sum of the angles of the filled sectors is equal to 1800, then the total area of the filled sectors will be equal to half the area of the circle.
2 Answer: = 2
5. Solve the inequality:
Solution:
1 6 + () = 2 6 + 6 2 = 0 Multiply by 6 (0) 62 + 1 2 6 = 0
Let's introduce the replacement = 6, then:
2 2 + 1 = 0 1,2 = 1
Back to replacement:
6 = 1 = 0 Answer: (, 0) (0, +).
6. Solve the equation tg. In the answer, write the smallest positive \u003d root.
(6) 1 Solution: Let =. Then =, = 6 +,.
(6) = + = 7 + 6, x(k) is an increasing function of k.
– – –
Let's find for each value of y the value of x:
2. y2=2 x=3 Answer: (2, 3), (3,2).
11. When publishing a book, it took 6949 digits to number its pages. How many pages are in the book?
– – –
12. On a round frying pan with a diameter of 30 cm, a pancake was baked in the form of a flat convex figure with an area of 400 cm2. Prove that the center of the pan is covered with a pancake.
Proof:
We will consider the frying pan as a circle with a diameter of 30 cm, and the pancake as a convex figure located inside the circle.
Find the area of the pan:
2 = 152 = 225 706.86 cm2 We get that the area of the pancake is more than half the area of the frying pan.
From the properties of convex figures it follows that through any point inside the pan and outside the pancake, you can draw a straight line that does not intersect the pancake.
We prove that the center of the pan is covered with a pancake. We prove by contradiction:
Suppose the center is not covered, then we draw such a straight line through it. Since the straight line does not intersect the pancake, and the pancake is completely on the pan, it turns out that the pancake is completely on one half of the pan. But the area of the pancake is larger than the area of half the pan. We got a contradiction. Hence the center of the pan is covered with a pancake.
13. The mother goose lined up her 4 goslings in one line, as she did before, to go to the nearest lake to dive and swim.
On their way to the lake, the goslings rearranged themselves and changed their original order.
Here's what we know about their new order:
1) Ha-Hee slowly rolls from foot to foot, but now no one will step on her heels, as Hee-Ha did before.
2) Ha-Ha ran to another place, because he does not like to go ahead of the "cutters" Ho-Ho.
3) Hee-ha goes where he usually goes.
4) The goose Ha-Ha will come to the lake first, and not Ha-Hi, as it happened before.
What was the previous order of the goslings and in what place will Ho-Ho be now?
Solution:
Under the conditions that the goose Ha-Ha will come to the lake first, and not Ha-Hi, as it happened before, we know that Ha-hee became the first. And knowing that Ha-Hi slowly rolls over from foot to foot, but now no one will step on her heels, as Hee-Ha did before, we get that Ha-Hee is now the last one. Ha-Ha moved to another place, because he does not like to go ahead of the "cutters" Ho-Ho, so Ho-Ho is not the second now. From the fact that Hee-Ha goes where he usually goes, we understand that the second one. We get that in the previous order it was like this: Ha-Hi - the first, Hee-Ha - the second, Ha-Ha - the third, and Ho-Ho - the fourth.
Accordingly, in the new order it became like this: Ha-Ha - the first (from condition 4), Hee-Ha - the second (from condition 3), Ho-Ho - the third, Ha-Hee - the fourth (from condition 1).
Therefore, Ho-Ho became the third.
14. Anya had a lot of friends at her birthday party. When the guests began to chat, they noticed that the number of guests who are familiar with an odd number of invitees is even. Anina's best friend made the statement that this pattern is true for any company. Prove it is.
Solution:
Let us denote the number of friends who have an odd number of acquaintances in the company as k, and, accordingly, the number of acquaintances of these friends as a1, a2,…, ak. In addition, the number of friends who know an even number of members of the company will be denoted by n, and the number of acquaintances of these friends, respectively, by b1, b2, …, bn. Based on this, then the total number of acquaintances is equal to (a1 + a2 +…+ ak + b1 + b2 +…+ bn)/ 2.
The sum b1 + b2 +…+ bn is even, since all its terms are even.
In order for this fraction to be equal to an integer, the sum a1 + a2 +…+ ak must be even. But all terms of the last sum are odd, so the number k of terms in the sum can only be even.
15. Nimble pirates Captain Blood and Captain Hook, having dug up the entire uninhabited island, still found a treasure chest. When they opened it, they saw in it 17 coins, 2 rings and 1 crown. All this wealth was divided among themselves by equal parts by weight of Blood and Hook. Moreover, the crown went entirely to Hook. Coins and rings were also not cut into pieces. One coin is as much heavier than one ring as one coin is lighter than one crown. How many coins and rings does Blood have?
