There are many tables and many people in one room. Math Problem .

Set to n people, from the title:

n+1 is just divisible by .

So n+1 is a common multiple of .

Since the least common multiple of is 5 7 9 = 315

So n+1 = 315k, (k is a positive integer).

And since n is a multiple of 11, we get n = 11m, (m is a positive integer), so there is: 11m+1 = 315k

When k = 8, there is m = 229 to meet the requirements, at this time n = 2519, that is, a total of 2519 people.

Note: When k=19, n=5984 meets the requirements.

When k=30 meets the requirements.

That is, when k = 11a + 8 (a is a natural number), the requirements are satisfied.

Because the multipliers of m and k are , when 11m+1 = 315k, there is 11(m+315)+1 = 315(k+11), so strictly speaking, this problem is not the only solution.

Regardless of the last condition, if there is one more person, it is a common multiple of 3,5,7,9, then the minimum is 945-1=944 people.

But 944 divided by 11 is more than 9is not a multiple of 11, at this time you need to add n 945 people to meet the topic.

When 944+945 9=9449 satisfies the topic.

That is, what is sought.

As it says upstairs, it must be a common multiple of , but a multiple of 9 must be a multiple of 3, so it must be a multiple of 5, 7, 9 = 315, and then subtract by one, when 315 8-1 = 2519.

Answer: First of all, according to the meaning of the question, it can be seen that if one more person is added, the tables of 3,5,7,9 people can be just filled, and the tables of 11 people will have one more person, so the least common multiple of the ball 3,5,7,9 is 315, and if there are x tables and the number of people is 315y, then the equation is obtained from the question:

11x=315y-1；

I program in C as follows:

for(x=1;x<=1000;x++)

The calculations result in x = 859 and y = 315, so the total number of people is 9449 and there are 859 tables.

There are countless solutions to this problem.

Answer: 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.

Remember to adopt it

There are titles that can be seen:

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 Not divisible by 11 315 2-1=629 Not divisible by 11 315 3-1=944 Not divisible by 11......315 8-1=2519 2519 11=229, so the number of people is 2519 and the table is 229

No solution, someone calculated that the table 229 people 2519 first of all is not satisfied 3x+2=y Don't waste brain cells The question is wrong.

The way this problem is understood should be the basis for the final calculation, and the question should be designed to be, 'If the above conditions are met, please calculate the minimum number of tables in the house?' Or, 'If you meet the above criteria, count the minimum number of people in the house?' ’

Because this is an interview question for human resources recruitment, it is mainly a test of thinking mode, not calculation ability.

Please read the topic clearly, (Say that there are multiple tables in a room, how many people?) I didn't ask how many tables there were!! Sweat.

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

3x+2=y x=839

5x+4=y x=503

7x+6=y x=359

9x+8=y x=279

11x=y x=229

x is not the same y=2519

A: There are at least 2,519 people in this room.

There are x people in the house, then.

If 3 people one.

table, 2 more people.

If there are 5 people per table, there are 4 more people.

If there are 7 people per table, there are 6 more people.

If there are 9 people per table, there are 8 more people.

If there are 11 people at a table, it is exact.

If a person comes in, then.

If there are 3 people at a table, it is exact.

If there are 5 people per table, it is exact.

If there are 7 people at a table, it is exact.

If there are 9 people at a table, it is exact.

If there are 11 people at a table, there is one more person.

That is, x+1 is divisible by 3, 5, 7, and 9 at the same time.

Because the least common multiple of 3,5,7,9 is 315

Then x+1=315n, where n is a positive integer.

x=315n-1

x is divisible by 11.

i.e. (315n-1) 11 = integer.

When n=8 is obtained, the above equation is taken as an integer.

So the number of people in the house is 315 * 8-1 = 2519 people.

2519。With x people, if you add one person, x+1 is divisible by 3,5,7,9. It's a multiple of 315, set to n times.

The remainder of 315 divided by 11 is 7, and for x to be divisible by 11, only 7n-1 is divisible by 11. n=8, this number is 315*8-1=2519

【Analysis】From the meaning of the title, it can be seen that the number of people is a common multiple of 3, 5, 7, and 9, a number less than 1, and a multiple of 11, and the number that meets both conditions is found

Solution: The least common multiple of 3,5,7,9 is 5 7 9 = 315, 315-1 = 314, 314 is not a multiple of 11, which is not in line with the topic;

315 2-1=629, 629 is not a multiple of 11, it is not on topic;

315 3-1=944, 944 is not a multiple of 11, it is not on topic;

315 4-1=1259, 1259 is not a multiple of 11, it is not on topic;

315 5-1=1574, 1574 is not a multiple of 11, it is not on topic;

315 6-1=1889, 1889 is not a multiple of 11, it is not on topic;

315 7-1=2204, 2204 is not a multiple of 11, it is not on topic;

315 8-1=2519, 2519 is a multiple of 11, which is in line with the title So there are 2519 people in this room

Note: This question examines divisors and multiples, and the key to solving the problem is to clarify that the number of people is a common multiple of 3, 5, 7, and 9, a number less than 1, and a multiple of 11

There is a chapter X table in the room. There are 11x people in total. Because a table of 3 people is more than 2, 5 more than 4, 7 more than 6, 9 more than 8.

So in other words, if there is one more person in the total number, then whether there are 3 or 5 or 7 or 9 people per table, there will be one more table without many people. Therefore, with 1 more person, the total number of people is 11x+1. This number is exactly n times the least common divisor of .

This least common divisor = 5 * 7 * 9 = 315. Column equation: 11x+1=315n n takes an integer from 1, when n=8 meets the equation condition, the solution is x=229, so the total number of people = 11*229=2519 229 tables.

That is, these people are divisible by 3 by 2, 5 by 5 by 4, 7 by 7 by 6, 8 by 8 by 7 by 7 and 7 by 11. That's a lot of money. I'll think about it first--

The least is also: 2,519 people.

This sequence is:

In this question, you must first find out how many tables are used.

Table for 3 people: 5 7 9 = 315 sheets

Table for 5 people: 3 7 9 = 189 sheets

7-person table: 3 5 9=135 sheets

Tables for 9 people: 3 5 7 = 105 sheets

Find out how many people there are based on the number of tables used.

3-person table 315=945

Table for 5 people 189=945

Table for 7 people 135=945

9 people table 105=945

According to the title, 11 people at a table are just right, and how many people are in total:

945 + 1 = 946 people.

946 people 11 people = 86 tables

Verification: 3 people and 2 more people at the table.

Validation: 5 people and 4 more people at the table.

5 people 189+1 -946=4

Validation: 7 people More than 6 people at the table.

Table for 7 people 135+1 -946=6

Verification: 9 people and 8 more people at the table.

9 people 105+1 -946=8

Verification: 11 people The table is just right.

946 people 11 people = 86 tables

A: There are 946 people and 316 tables.

3*5*7*9-1=944

944 11 Incomplete (Wrong Title!) ）

944 8 = 118 (exactly divided).

The topic should be 8 people per table.

This is a question of enumeration. If the number of tables is n, then the number of people m n = 3 and 2. So, when n=1, the number of people m=5

When n=2, the number of people m=2*3+2=8

When n=3, the number of people m=3*3+2=11

When n=4, the number of people m=3*4+2=14

When n=5, the number of people m=3*5+2=17.

Any combination is true.

5 more than 4 words.

First of all, from the topic, we know that the number of people is a multiple of 11, and if the total number of people is added to one person, it is a multiple.

So, assuming that this total number of people is x, then, x+1 is a multiple of 9, a multiple of seven, a multiple of five, and a multiple of three, and 9 is a multiple of 3 and is negligible.

So x+1 must be a multiple of 9*7*5=315.

Then substituting, x+1=315y, and then using the substitution method, when y is equal to a few, x is a multiple of 11. That's it, and finally get, when y=8, that is, x+1=315*8=2520, x=2520-1=2519 is just a multiple of 11.

There are infinite solutions to this.

The minimum is 2519

Dear, your questions are not complete

According to the topic. +1 is exactly divisible by at the same time, so the number of people must be .

A common multiple is a multiple of 315.

The number of people is 315m-1 (m is an integer not less than 1).

That is, the number of people is 314,629,944,1259,1574,1889,2204,2219,2534,2849....

The smallest digit divisible by 11 is 2849, and it is thought that 315 is not divisible by 11, so the number of people is 2849 + 315 * 11m = 2849 + 3465m (m is an integer not less than 0).

Assuming that the original minimum number of people is x, then (x+1) is a multiple of , and the least common multiple of the 4 numbers is 315, and then try.

x=n*315-1，（n
、。Until it is divisible by 11, the minimum number of people calculated is 2519

This is a question of enumeration. If the number of tables is n, then the number of people m n = 3 and 2. So, when n=1, the number of people m=5

When n=2, the number of people m=2*3+2=8

When n=3, the number of people m=3*3+2=11

When n=4, the number of people m=3*4+2=14

When n=5, the number of people m=3*5+2=17.

Any combination is true.

If there is a group of people in a room, if there are 2 more people at a table for 3 people, 4 more people at a table for 5 people, 6 more people at a table with 7 people, 8 more people at a table with 9 people, and a table with 11 people is just full.

Analysis: From the meaning of the title, it can be seen that the number of people is a common multiple of 3, 5, 7, and 9, a number less than 1, and a multiple of 11

Solution: The least common multiple of 3,5,7,9 is 5 7 9 = 315, 315-1 = 314, 314 is not a multiple of 11, which is not in line with the topic;

315 2-1=629, 629 is not a multiple of 11, it is not on topic;

315 3-1=944, 944 is not a multiple of 11, it is not on topic;

315 4-1=1259, 1259 is not a multiple of 11, it is not on topic;

315 5-1=1574, 1574 is not a multiple of 11, it is not on topic;

315 6-1=1889, 1889 is not a multiple of 11, it is not on topic;

315 7-1=2204, 2204 is not a multiple of 11, it is not on topic;

315 8-1=2519, 2519 is a multiple of 11, which is in line with the title, so there are 2519 people in total.

Tables: 2519 11 229 (sheets).