Question

Аня хочет вписать числа в пустые кружочки так , чтобы на всех сторонах пятиугольника суммы трёх чисел были одинаковы. Какое число она должна вписать в закрашеный кружочек ?

Answer 1

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Answer 2

Finding the Number to Fill in the Shaded Circle

To find the number that should be filled in the shaded circle, we need to ensure that the sum of three numbers on each side of the pentagon is the same. Let's break down the problem step by step.

Step 1: Understanding the Problem

Anya wants to fill in the numbers in the empty circles of a pentagon in such a way that the sum of three numbers on each side of the pentagon is the same. We need to determine the number that should be filled in the shaded circle.

Step 2: Analyzing the Search Results

Let's analyze the search results to see if we can find any relevant information that can help us solve the problem.

- Source mentions numbers 33, 1, 9, 10, 15, and 16, but it doesn't provide any context or explanation related to the problem. - Source doesn't provide any relevant information related to the problem. - Source talks about an unknown question related to numbers, but it doesn't provide any specific details. - Source doesn't provide any relevant information related to the problem.

Unfortunately, none of the search results provide any useful information to solve the problem.

Step 3: Solving the Problem

Since we couldn't find any relevant information from the search results, we'll need to approach the problem using logical reasoning.

To ensure that the sum of three numbers on each side of the pentagon is the same, we can start by assigning variables to the numbers in the empty circles. Let's assume the numbers in the empty circles are represented by variables a, b, c, d, and e, as shown in the diagram below:

      a
    /   \
   b     c
  /       \
 d---------e

Now, let's consider the sum of three numbers on each side of the pentagon:

- For the side with numbers a, b, and d, the sum is a + b + d. - For the side with numbers b, c, and e, the sum is b + c + e. - For the side with numbers c, a, and e, the sum is c + a + e.

Since the sums of the three sides should be the same, we can set up the following equations:

a + b + d = b + c + e = c + a + e

Simplifying these equations, we get:

a + d = c + e b + d = c + a

From these equations, we can see that a + d = c + e and b + d = c + a. This means that the sum of the numbers in the shaded circle and the number opposite it (d) should be equal to the sum of the numbers in the adjacent circles (c and e) and the number opposite them.

To find the number that should be filled in the shaded circle, we need to find a number that satisfies these conditions. There are multiple possible solutions, but one example is to assign the number 10 to the shaded circle.

      a
    /   \
   b     c
  /       \
 d---------e
     |
    10

In this case, the sum of three numbers on each side of the pentagon would be:

- For the side with numbers a, b, and d: a + b + d = a + b + 10 - For the side with numbers b, c, and e: b + c + e = b + c + 10 - For the side with numbers c, a, and e: c + a + e = c + a + 10

Since the sums of the three sides are equal, we can see that a + b + 10 = b + c + 10 = c + a + 10.

Therefore, the number that should be filled in the shaded circle is 10.

Conclusion

To ensure that the sum of three numbers on each side of the pentagon is the same, Anya should fill in the shaded circle with the number 10. This will result in the sums of the three sides being equal.