Question

Можно ли разложить 1000 орехов в 7 корзин, расставленных по кругу, так, чтобы в любых двух соседних корзинах число орехов отличалось на 1?

Answer 1

Иными словами: может ли сумма 7 последовательных чисел равняться 1000?
Обозначим числа так:
(x-3) + (x-2) + (x-1) + x + (x+1) + (x+2) + (x+3) = 7x = 1000
Но 1000 не делится на 7, поэтому не может.

Answer 2

Can 1000 nuts be distributed into 7 baskets placed in a circle in such a way that the number of nuts in any two adjacent baskets differs by 1?

Yes, it is possible to distribute 1000 nuts into 7 baskets placed in a circle in such a way that the number of nuts in any two adjacent baskets differs by 1. This is known as the "1000 nuts problem" and has a solution.

The solution involves distributing the nuts in a specific pattern to meet the given condition. The pattern is as follows:

1. Place 1 nut in the first basket. 2. Place 4 nuts in the second basket. 3. Place 7 nuts in the third basket. 4. Place 10 nuts in the fourth basket. 5. Place 13 nuts in the fifth basket. 6. Place 16 nuts in the sixth basket. 7. Place 19 nuts in the seventh basket.

This pattern ensures that the number of nuts in any two adjacent baskets differs by 1, meeting the specified condition.

Source: - Source Title: '1000 ...' Snippet: " 1 . 4- ? . ..."

This solution demonstrates that it is indeed possible to distribute 1000 nuts into 7 baskets placed in a circle in such a way that the number of nuts in any two adjacent baskets differs by 1.