How many people are in this room, and how many people are in the room?

As can be seen from the title:

Number of people + 1) is divisible by 3,5,7,9, so (number of people + 1) is a common multiple of 3,5,7,9, and their least common multiple is 315, so the number of people should be a multiple of 315 minus 1, i.e. :

Number of people = 315 n-1

From the last sentence, we can know that the number of people is divisible by 11.

So you can try that multiple of 315 to meet this condition:

315-1=314 is not divisible by 11.

315 2-1=629 is not divisible by 11.

315 3-1=944 is not divisible by 11.

315 8-1=2519 - 11 people per table: 2519 11=229 tables.

So the minimum number of people is 2519, and if you can sit down, the table is 2519 3+1 is equal to 840

This problem should be calculated like this: from the last point of the condition, you can set the number of people to be 11n, pull a waiter to sit in, one, two, three and four problems are solved, then 11n+1 is a common multiple of , that is, it can be expressed as 11n 1 315k, this problem is solved a lot, the minimum value is k=8 when n=2519, so the minimum number of people in this problem should be 2519, the standard value is 5 7 11 9 m 2519, that is, the answer to this question is 3465m+2519 where m is a non-negative integer, when m=0 is 2519, 5984 when m=1, and ...... when m=2, the same problem can be seen in the problem of the three brothers dividing the cow!

Solution 1:

So the total number of people should be 315m-1

and 11|315m-1 (11 divisible by 315m-1) 315*8-1=2519

and 11|2519

So there are at least 2,519 people.

2519 11 = 229 (sheets).

So there are 229 tables in the room.

A: There are 2,519 people in this room and there are 229 tables.

Solution 2: Solution: Set up this room with x tables and y people.

3x+2=y

5x+4=y

7x+6=y

9x+8=y

11x=y is connected to five equations.

Solution: x=229

y=2519

A: There are 2,519 people in this room and there are 229 tables.

So the total number of people should be 315m-1

and 11|315m-1 (11 divisible by 315m-1) 315*8-1=2519

and 11|2519

So there are at least 2,519 people.

2519 11 = 229 (sheets).

So there are 229 tables in the room.

A: There are 2,519 people in this room and there are 229 tables.

Solution: Solution: Let this room have x tables and Y people.

3x+2=y

5x+4=y

7x+6=y

9x+8=y

11x=y is connected to five equations.

Solution: x=229

y=2519

A: There are 2,519 people in this room and there are 229 tables.

It's an interesting question, because if you add one more person, it's exactly a multiple of 3. The number of people is x=5*7*9*n-1=. （n=1,2,3...

x must also be a multiple of 11. From this, when n=8 is obtained, the condition is exactly met. The number of people is 315*8-1=2519.

Tables are 2519 11 = 229 sheets.

Hello, it can be understood by the Chinese surplus.

However, the remainder of this problem is special: all except 11 are -1 (1 less than the divisor), so first find 3 5 7 9 Least common multiple: 315

Subtract 1 more to get 314

Numbers that match 3 5 7 9: 315k-1 k>0 is an integer, then look at 11 314 and the remainder is 6

Therefore, for 11 315k-1 7k-1 and 7k-1, it is a multiple of 11 for 7k-1.

If you add 1 person, then 3, 5, 7, 9 people are all sitting exactly the common multiple of the number of people at this time, and the least common multiple of 1 person more than the multiple of 11 is 315,315 11 = 28....7 people, not up to the mark.

Because to ensure that it is a common multiple of , 315 people should be added each time, that is, the remainder should be increased by 7 each time

The multiple of 7 is divided by 11 and the minimum is 8 times 7 (56), so the number of people at this time is at least 315 8 = 2520 people.

The original number of people is at least: 2520-1=2519 people, the table may not be counted, the table used for each sitting method is different, and the room is too big.

Let the number of people be x, then x+1 is a common multiple of 3,5,7,9, and the least common multiple of 3,5,7,9 = 5 7 9 = 315, so the number of people in the state is 315n-1, and the number of people is a multiple of 11, so there are 315n-1=11m (m is the number of tables with people), when n=8, m=229, and 315n-1=11m=2519 (people) in this reading, so when the number of people is the least, x=315n-1 are all answers that meet the question.

3*（3*5*7*（8+11*n）-1）+2 = 5*（7*9*（8+11*n）-1）+4 = 7*（5*9*（8+11*n）-1）+6 = 9*（5*7*（8+11*n）-1）+8

where n is a natural number. So when there are least people n = 0, the number of people is equal to 2519. There are 11 people and 229 tables per table.

When n=1, the number of people is 5984, and when n=2, the number of people is 9449,,,12914,16379,19844,23309,26774,..

The tables of three people, five people, seven people, and nine people are just full. The least common multiple of 3,5,7,9 is 315

So the number of people is 315n-1Because a table of 11 people is just full, 11m = 315n-1 = (11 * 28 + 7) n-1

m=28n+(7n-1)/11

When n=8, m=229

There are a total of 229*11=2519 people.

This problem should be calculated like this: from the last point of the condition, you can set the number of people to be 11n, pull a waiter to sit in, one, two, three or four problems are solved, then 11n+1 is a common multiple of , that is, it can be expressed as 11n 1 315k, this problem is solved a lot, the minimum value is k = 8 when n = 2519, so the minimum number of people in this problem should be 2519, the standard value is 5 7 11 9 m 2519 The problem can be seen in the problem of three brothers dividing the cow!

The answer is not the same in two ways of understanding.

In the first type of ten people, there is a couple who sit randomly around a round table and find out the probability that the couple is exactly next to each other.

The probability of 2 9 can be understood in this way: when the man sits well, the woman still has nine seats left to choose, of which there are 2 adjacent to the man, so the probability of adjacency is 2 9, and no matter what seat the man sits, this probability will not change.

The number of possible scenarios in which n people randomly sit around a round table is n!/n = (n-1)!There are two cases where two people are tied together, and the number of possible cases in which (n-1) an individual randomly sits around a round table is (n-1)!

n-1) = (n-2)!Then the number of cases where two people sit together is 2 * n-2)!So this probability is 2 * n-2)!

(n-1)! = 2/(n-1)

The second idea is the round table, so your total event at the beginning is 10!No, if it's round, it's the same 12345678910 as 23456789101!Therefore, I can't use the alignment of the station pair!

The final result should be 2 9!It's very simple, let's say the husband and the others sit down first, and do it last, which is also a jack, then the wife can choose nine positions, and two of the positions are connected to the husband, so it's 2 9.