Question

Детям 15, 8, 5, 13 лет. Их имена Ваня, Оля, Витя, Гена. Сколько лет каждому из них, если один мальчик ходит в детский сад, Ваня старше Оли, если сложить возраст Вани и Вити, число будет делиться на 3.

Answer 1

Вити5
Оле8
Ваня13
Гена15

Answer 2

Вите 5
Оле 8
Ване 13
Гене 15

Answer 3

Calculation of Ages

To determine the ages of the children, let's analyze the given information:

- One boy goes to kindergarten. - Vanya is older than Olya. - The sum of Vanya's and Vitya's ages is divisible by 3.

Let's break down the information step by step:

1. One boy goes to kindergarten. This means that the child who goes to kindergarten is either Vanya, Olya, or Gena. We don't have enough information to determine which one it is.

2. Vanya is older than Olya. This means that Vanya cannot be the youngest child, as the youngest child is 5 years old. Therefore, Vanya must be either 8, 13, or 15 years old.

3. The sum of Vanya's and Vitya's ages is divisible by 3. Let's consider the possible ages of Vanya and Vitya:

- If Vanya is 8 years old, Vitya can be 5, 13, or 15 years old. None of these combinations results in a sum divisible by 3. - If Vanya is 13 years old, Vitya can be 5, 8, or 15 years old. The sum of 13 and 15 is 28, which is divisible by 3. - If Vanya is 15 years old, Vitya can be 5, 8, or 13 years old. The sum of 15 and 8 is 23, which is not divisible by 3.

Therefore, the only combination that satisfies all the given conditions is if Vanya is 13 years old and Vitya is 15 years old.

Based on this information, we can determine the ages of the children as follows:

- Vanya: 13 years old - Olya: We know that Vanya is older than Olya, so Olya must be either 5 or 8 years old. Since the youngest child is 5 years old, Olya is 5 years old. - Vitya: We know that Vitya is the child whose age, when added to Vanya's age, is divisible by 3. Since Vanya is 13 years old, Vitya must be 15 years old. - Gena: The remaining child is Gena, who must be 8 years old.

Therefore, the ages of the children are as follows:

- Vanya: 13 years old - Olya: 5 years old - Vitya: 15 years old - Gena: 8 years old

Note: The information provided does not specify which child goes to kindergarten.