# Task No. 6.4

## Condition:

On the faces of a cube, 6 letters are drawn: A, B, V, G, D, E. The picture shows three images of the cube from different angles. Which letter is drawn on the face opposite the face with the letter $\mathrm{A}$?
![](https://cdn.mathpix.com/cropped/2024_05_06_4cfa7cdc7a8a51b9e752g-25.jpg?height=306&width=870&top_left_y=678&top_left_x=593)

## Answer Options:

○ A

$\circ$ B

$\circ$ V

$\circ$ G

$\circ$ D

○ E

## Correct Answer:

○ B

Exact match of the answer - 1 point
Solution by analogy with problem №6.1.

## Condition:

Anya, Borya, and Vasya took the same test consisting of 6 questions, each of which can be answered with "yes" or "no." The answers are presented in the table:

| Question No. | 1 | 2 | 3 | 4 | 5 | 6 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| Anya | no | no | yes | yes | yes | yes |
| Borya | yes | no | no | yes | yes | yes |
| Vasya | no | yes | no | no | no | no |

It turned out that Anya has two incorrect answers, and Borya has only two correct answers. How many correct answers does Vasya have?

Answer: 3

Exact match of the answer - 1 point

## Solution.

Anya has 4 correct answers, and Borya has 2. Therefore, there are at least two questions on which Anya answered correctly, and Borya answered incorrectly. However, Anya and Borya gave different answers to exactly two questions: the first and third. Therefore, it is precisely on these questions that Anya answered correctly, and Borya answered incorrectly. Vasya's answer to the first question matches Anya's, and on the third question, it does not. Therefore, among these two of Vasya's answers, exactly one is correct. Anya's and Borya's answers to the four remaining questions coincide. Therefore, among them, two are correct and two are incorrect. Vasya's answers to all these questions are opposite to Anya's and Borya's. Therefore, among them, two are correct (where Anya and Borya's answers are incorrect) and two are incorrect (where Anya and Borya's answers are correct). Adding 1 and 2, we get the answer.

## Condition:

Anya, Borya, and Vasya took the same test consisting of 6 questions, each of which can be answered with "yes" or "no." The answers are presented in the table:

| Question No. | 1 | 2 | 3 | 4 | 5 | 6 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| Anya | yes | no | no | yes | no | yes |
| Borya | no | no | yes | yes | no | yes |
| Vasya | no | yes | no | no | yes | no |

It turned out that Anya has two incorrect answers, and Borya has only two correct answers. How many incorrect answers does Vasya have?

Answer: 3

Exact match of the answer - 1 point

Solution by analogy with problem №7.1.

## Condition:

Anya, Borya, and Vasya took the same test consisting of 6 questions, each of which can be answered with "yes" or "no." The answers are presented in the table:

| Question No. | 1 | 2 | 3 | 4 | 5 | 6 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| Anya | no | no | yes | yes | yes | yes |
| Borya | yes | no | yes | yes | yes | no |
| Vasya | no | yes | no | no | no | no |

It turned out that Anya has two incorrect answers, and Borya has only two correct answers. How many correct answers does Vasya have?

Answer: 3

Exact match of the answer - 1 point

Solution by analogy with problem №7.1.