Question

Оля купила пакетик орехов. Когда Оля съела два ореха, число оставшихся орехов стало делиться на 4. Оля съела ещё один орех, и оказалось, что число оставшихся орехов стало делиться на 3. Сколько ещё орехов придётся съесть Оле (как можно меньше), чтобы все оставшиеся орехи она смогла раздать поровну своим шести подругам?

Answer 1

Пошаговое объяснение:

Поскольку , когда Оля съела 2 ореха , число оставшихся орехов стало делиться на 4 ,то сначала у Оли было четное число орехов.

После того как она съела еще 1 орех, число оставшихся стало делиться на 3 , значит число оставшихся стало нечетным, а значит не будет делится на 6 ( признак делимости на 6 : число делится на 6 если оно одновременно делится на 2 и на 3).

Если Оля съест еще 1 орех , то число станет четным и не будет делится на 3 .

Если Оля съест еще 2 ореха , то число будет нечетным и не будет делится на 3 .

А вот если Оля съест еще 3 ореха, то число будет четным и будет делится на 3, а значит будет делиться на 6 .

Оле необходимо съесть еще 3 ореха, чтоб оставшиеся орехи она могла разделить поровну между шестью своими подругами

Answer 2

#### Problem Analysis To solve this problem, we need to determine the number of additional nuts Olga needs to eat so that she can distribute the remaining nuts equally among her six friends. We are given that when Olga ate two nuts, the remaining number of nuts became divisible by 4. When she ate one more nut, the remaining number of nuts became divisible by 3. Let's assume the initial number of nuts Olga bought is represented by the variable `x`. After eating two nuts, the remaining number of nuts is `(x - 2)`. We know that `(x - 2)` is divisible by 4. Similarly, after eating one more nut, the remaining number of nuts is `(x - 3)`, which is divisible by 3. To find the solution, we need to determine the smallest possible value of `x` that satisfies both conditions. #### Solution Let's analyze the given conditions: 1. `(x - 2)` is divisible by 4. 2. `(x - 3)` is divisible by 3. To find the smallest possible value of `x`, we can start by checking multiples of 4 and 3 until we find a number that satisfies both conditions. Let's start with the smallest multiple of 4, which is 4 itself. If we subtract 2 from 4, we get 2, which is not divisible by 4. Therefore, 4 is not a valid solution. Next, let's try the next multiple of 4, which is 8. If we subtract 2 from 8, we get 6, which is divisible by 4. Now, let's check if `(x - 3)` is divisible by 3. If we subtract 3 from 8, we get 5, which is not divisible by 3. Therefore, 8 is not a valid solution. We continue this process until we find a valid solution. #### Checking Multiples of 4 and 3 Let's check the multiples of 4 and 3 to find a valid solution: - 12: `(12 - 2) = 10` (not divisible by 4), `(12 - 3) = 9` (not divisible by 3) - 16: `(16 - 2) = 14` (not divisible by 4), `(16 - 3) = 13` (not divisible by 3) - 20: `(20 - 2) = 18` (not divisible by 4), `(20 - 3) = 17` (not divisible by 3) - 24: `(24 - 2) = 22` (not divisible by 4), `(24 - 3) = 21` (divisible by 3) We have found a valid solution: 24. When Olga eats two nuts, the remaining number of nuts is 22, which is divisible by 4. When she eats one more nut, the remaining number of nuts is 21, which is divisible by 3. Therefore, Olga needs to eat **24** nuts in total so that she can distribute the remaining nuts equally among her six friends. #### Conclusion Olga needs to eat a total of 24 nuts so that she can distribute the remaining nuts equally among her six friends.