Question

Сколько в кабинете двухместных парт, если известно, что: 1) как бы учащиеся 5 – А класса, в котором 30 человек, не сели, на не более чем на 10 партах окажется количество учащихся, отличное от двух; 2) как бы учащиеся математического кружка, в котором 13 человек, не сели, не менее чем 6 парт окажутся свободными; 3) учащиеся 5 –Б класса, в котором 26 человек, могут сесть так, что заняты будут все парты, а по двое будут сидеть на четном количестве парт?

Answer 1

1: 3 парты
2: 4 двух местных и 1 одноместная
3: 14 двух местных и 12 одноместных

Answer 2

Calculation of the Number of Two-Seater Desks in the Classroom

To determine the number of two-seater desks in the classroom, we need to consider three scenarios:

1. Scenario 1: Class 5-A with 30 students, where no more than 10 desks are occupied. 2. Scenario 2: Mathematics Circle with 13 students, where at least 6 desks are unoccupied. 3. Scenario 3: Class 5-B with 26 students, where all desks are occupied and two students sit on an even number of desks.

Let's calculate the number of two-seater desks for each scenario:

1. Scenario 1: Class 5-A with 30 students - In this scenario, no more than 10 desks are occupied. - We need to find a number that is less than or equal to 10 and not divisible by 2. - The possible numbers are 1, 3, 5, 7, and 9. - Therefore, the number of two-seater desks in this scenario is 5.

2. Scenario 2: Mathematics Circle with 13 students - In this scenario, at least 6 desks are unoccupied. - We need to find a number that is greater than or equal to 6 and not divisible by 2. - The possible numbers are 7 and 9. - Therefore, the number of two-seater desks in this scenario is 7 or 9.

3. Scenario 3: Class 5-B with 26 students - In this scenario, all desks are occupied, and two students sit on an even number of desks. - We need to find a number that is divisible by 2 and greater than or equal to 26. - The possible numbers are 26, 28, 30, and so on. - Therefore, the number of two-seater desks in this scenario is 26 or any even number greater than or equal to 26.

To summarize: - In Scenario 1 (Class 5-A), there are 5 two-seater desks. - In Scenario 2 (Mathematics Circle), there are either 7 or 9 two-seater desks. - In Scenario 3 (Class 5-B), there are 26 or any even number greater than or equal to 26 two-seater desks.

Please note that the number of two-seater desks may vary depending on the specific requirements and arrangements in the classroom.