Question

По кругу расположены 15 занумерованных конфет- 1-я 2-я 3-я ... 15-я.Маша съедает какую-то конфету и затем, двигаясь по кругу, пропускает по ходу 2 конфеты и съедает третью, затем снова 2 пропускает и снова съедает третью, и так далее. С какой конфеты она должна начать, чтобы последней была съедена 15-я конфета?

Answer 1

С 3 конфеты просто нарисуй круг и вокруг него числа от1 до 15
и отмечай галочкой съеденые конфеты.
например:начнем с 15
15 пропускаем 2 будет12,
пропускаем еще 2 будет 10 и так до 3 конфеты которая завершает процесс!

Answer 2

Problem Analysis

Masha is eating candies arranged in a circle. She starts by eating one candy and then, while moving in a circle, skips two candies and eats the third one. She repeats this pattern until all the candies are eaten. We need to determine which candy Masha should start with so that the 15th candy is the last one to be eaten.

Solution

To solve this problem, we can use a mathematical approach. Let's assume that Masha starts with the x-th candy. We need to find the value of x.

We know that Masha eats one candy initially, so the total number of candies remaining is 14. After eating the first candy, Masha skips two candies and eats the third one. This means that after each round, the number of candies remaining decreases by 2.

To find the value of x, we can calculate the number of rounds it takes for Masha to eat all the candies. Since each round reduces the number of candies by 2, the number of rounds can be calculated as 14 / 2 = 7.

Now, we need to find the position of the 15th candy after 7 rounds. Since Masha starts at the x-th candy, the position of the 15th candy after 7 rounds can be calculated as (x + 7) % 15.

To find the value of x, we can iterate through all possible values from 1 to 15 and check if the position of the 15th candy after 7 rounds is equal to 15. The first value of x that satisfies this condition will be the answer.

Let's calculate the value of x using this approach:

1. Initialize a variable x with a value of 1. 2. Iterate through all possible values of x from 1 to 15. - Calculate the position of the 15th candy after 7 rounds using the formula (x + 7) % 15. - If the position is equal to 15, break the loop and store the value of x. 3. The value of x obtained from the loop will be the answer.

Let's calculate the value of x using this approach:

1. Initialize x with a value of 1. 2. Calculate the position of the 15th candy after 7 rounds using the formula (x + 7) % 15. 3. If the position is equal to 15, x is the answer. Otherwise, increment x by 1 and repeat steps 2 and 3. 4. The value of x obtained will be the answer.

Calculation

Let's calculate the value of x using the approach described above:

1. Initialize x with a value of 1. 2. Calculate the position of the 15th candy after 7 rounds using the formula (x + 7) % 15. - For x = 1, the position is (1 + 7) % 15 = 8 % 15 = 8. - For x = 2, the position is (2 + 7) % 15 = 9 % 15 = 9. - For x = 3, the position is (3 + 7) % 15 = 10 % 15 = 10. - For x = 4, the position is (4 + 7) % 15 = 11 % 15 = 11. - For x = 5, the position is (5 + 7) % 15 = 12 % 15 = 12. - For x = 6, the position is (6 + 7) % 15 = 13 % 15 = 13. - For x = 7, the position is (7 + 7) % 15 = 14 % 15 = 14. - For x = 8, the position is (8 + 7) % 15 = 15 % 15 = 0. - For x = 9, the position is (9 + 7) % 15 = 16 % 15 = 1. - For x = 10, the position is (10 + 7) % 15 = 17 % 15 = 2. - For x = 11, the position is (11 + 7) % 15 = 18 % 15 = 3. - For x = 12, the position is (12 + 7) % 15 = 19 % 15 = 4. - For x = 13, the position is (13 + 7) % 15 = 20 % 15 = 5. - For x = 14, the position is (14 + 7) % 15 = 21 % 15 = 6. - For x = 15, the position is (15 + 7) % 15 = 22 % 15 = 7. 3. The value of x that satisfies the condition is 8.

Answer

Masha should start with the 8th candy in order for the 15th candy to be the last one eaten.

Verification

Let's verify the answer by calculating the position of the 15th candy after 7 rounds, starting with the 8th candy:

1. Start with the 8th candy. 2. Calculate the position of the 15th candy after 7 rounds using the formula (8 + 7) % 15 = 15 % 15 = 0. 3. The position is 0, which means the 15th candy is the last one to be eaten.

The answer has been verified.

Conclusion

Masha should start with the 8th candy in order for the 15th candy to be the last one eaten.