# Task № 6.2

## Condition:

Anya, Tanya, and Vanya had identical cardboard squares with a side of 15 cm. Each of them cut off two rectangles from their square, as shown in the figure, and all 6 rectangles are the same. The perimeter of Anya's figure is 88 cm, and the perimeter of Vanya's figure is 80 cm.

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-22.jpg?height=337&width=349&top_left_y=557&top_left_x=251)

Anya

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-22.jpg?height=337&width=328&top_left_y=554&top_left_x=884)

Vanya

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-22.jpg?height=326&width=322&top_left_y=565&top_left_x=1478)

Tanya

Find the perimeter of Tanya's figure. Express your answer in centimeters.
Answer: 72

Exact match of the answer -1 point

Solution by analogy with task №6.1

## Condition:

Anya, Tanya, and Vanya had identical cardboard squares with a side of 16 cm. Each of them cut off two rectangles from their square, as shown in the picture, all 6 rectangles are the same. The perimeter of Anya's figure is 92 cm, the perimeter of Vanya's figure is 86 cm.

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-23.jpg?height=383&width=389&top_left_y=568&top_left_x=228)

Anya

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-23.jpg?height=379&width=371&top_left_y=570&top_left_x=840)

Vanya

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-23.jpg?height=389&width=397&top_left_y=565&top_left_x=1412)

Tanya

Find the perimeter of Tanya's figure. Express the answer in centimeters.

Answer: 80

Exact match of the answer -1 point

Solution by analogy with task №6.1

## Condition:

Anya, Tanya, and Vanya had identical cardboard squares with a side of 15 cm. Each of them cut off two rectangles from their square, as shown in the picture, all 6 rectangles are the same. The perimeter of Anya's figure is 84 cm, the perimeter of Vanya's figure is 76 cm.

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-24.jpg?height=366&width=368&top_left_y=571&top_left_x=227)

Anya

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-24.jpg?height=371&width=377&top_left_y=568&top_left_x=822)

Vanya

![](https://cdn.mathpix.com/cropped/2024_05_06_844ecc6fa8537977a6eag-24.jpg?height=385&width=391&top_left_y=567&top_left_x=1415)

Tanya

Find the perimeter of Tanya's figure. Express the answer in centimeters.

Answer: 68

Exact match of the answer -1 point

Solution by analogy with task №6.1

## Condition:

In the examples, each letter corresponds to a digit from 0 to 9. The same letters correspond to the same digits, different letters correspond to different digits.

$$
\begin{aligned}
& \text { L: E = T+O } \\
& \text { O+C=E } \times \mathbf{H}=\mathrm{b}
\end{aligned}
$$

What number is encoded by the following word?

## zero

Answer: 4368

## Exact match of the answer -1 point

## Solution.

Since $\mathrm{E} \times \mathrm{H}=\mathrm{b}$, then b can only be 8 or 6: 8 = 2 * 4, or 6 = 2 * 3.

If $\mathrm{b}=6$, then $\mathrm{E}$ and $\mathrm{H}$ are 2 and 3 in some order. $\mathrm{O}+\mathrm{C}=6$, this can only be 1 + 5 or 5 + 1 (0 + 6, 2 + 4, and 3 + 3 do not work, as 2, 3, and 6 are already used). Then the sum $\mathrm{T}+\mathrm{O}$ is at least 4 + 1 = 5 (0 + 1 cannot be the result of dividing L by E, and 2 and 3 are already used). But the result of dividing a single-digit number L by 2 or 3 is less than 5, a contradiction.

Then $\mathrm{b}=8$, and $\mathrm{E}$ and $\mathrm{H}$ are 2 and 4 in some order. E cannot be 4, as there is no other digit besides 8 that is divisible by 4, for the letter L. Therefore, $\mathrm{E}=2, \mathrm{H}=4$. The only even digit left for the letter L is 6. We get that $6: 2=\mathrm{T}+\mathrm{O}, \mathrm{O}+\mathrm{C}=2 \times 4=8$ and the unused digits are 0, 1, 3, 5, 7, and 9. Since $\mathrm{T}+\mathrm{O}=3$, this is 3 + 0 or 0 + 3, but if $\mathrm{O}=0$, then $\mathrm{C}=8$, and 8 is already used, so $\mathrm{O}=3, \mathrm{~T}=0$ and $\mathrm{C}=5$.

The word ZERO then corresponds to the number 4368.

## Condition:

In the examples, each letter corresponds to a digit from 0 to 9. The same letters correspond to the same digits, different letters correspond to different digits.

$$
\begin{aligned}
& \text { L: } \mathrm{E}=\mathrm{T}+\mathrm{O} \\
& \mathrm{O}+\mathrm{C}=\mathrm{E} \times \mathrm{H}=\mathrm{b}
\end{aligned}
$$

What number is encoded by the following word?

## ELEPHANT

Answer: 5634

Exact match of the answer -1 point

Solution by analogy with task №7.1

## Condition:

In the examples, each letter corresponds to a digit from 0 to 9. The same letters correspond to the same digits, different letters correspond to different digits.

$$
\begin{aligned}
& \text { L: } \mathrm{E}=\mathrm{T}+\mathrm{O} \\
& \mathrm{O}+\mathrm{C}=\mathrm{E} \times \mathrm{H}=\mathrm{b}
\end{aligned}
$$

What number is encoded by the following word?

## salt

Answer: 5368

Exact match of the answer -1 point

Solution by analogy with task №7.1

## Condition:

In the examples, each letter corresponds to a digit from 0 to 9. The same letters correspond to the same digits, different letters correspond to different digits.

$$
\begin{aligned}
& \text { L: } \mathrm{E}=\mathrm{T}+\mathrm{O} \\
& \mathrm{O}+\mathrm{C}=\mathrm{E} \times \mathrm{H}=\mathrm{b}
\end{aligned}
$$

What number is encoded by the following word?

$$
\text { C ET b }
$$

Answer: 5208

Exact match of the answer -1 point

Solution by analogy with task №7.1