Решение задач олимпиады

It looks like you've uploaded several images of questions from an olympiad in Informatics. Let me help you solve them one by one.

Let's start with the first question:

Задание 2 (Question 2)

Question: How many natural numbers $x$ are there that are greater than the binary number $01111101_2$ and less than the hexadecimal number $8F_{16}$?

To solve this:

1. Convert $01111101_2$ to decimal: $01111101_2 = 125_{10}$.

2. Convert $8F_{16}$ to decimal: $8F_{16} = 8 \times 16 + 15 = 143_{10}$.

3. We need to find how many natural numbers are greater than 125 and less than 143. These are the numbers 126 to 142.

4. Count the numbers: $142 - 126 + 1 = 17$.

The answer for this question seems to be missing from the options, so the correct choice would be "Correct answer is missing."

Let me know if you'd like me to proceed with the next question!

The sum of the weights of the edges $АГ$ (A-G) and $ВЖ$ (B-ZH) is 18. Let me know if you'd like further clarification or help with the next question!

Let's go step by step for the task.

Задание 5 (Question 5)

Problem:
We have domino stones set up in a line such that if one stone falls, the others will also fall in sequence. The goal is to determine which stone and in which direction should be pushed to make the maximum number of stones fall.

To solve this:

1. Initial Table Values: Each domino has an (x, h) pair where x is the position and h is the height.

2. The Key Insight:
   The stone you push will fall and then trigger other stones to fall, provided the height difference between the current stone and the next is positive (greater height will push the next one). So, we need to check which direction yields the highest number of falling stones.

3. Calculating the Right Direction:

   • If you push to the right, each stone must be taller than the next for it to fall.
   • If you push to the left, the opposite condition must be true: each stone must be shorter than the previous stone for it to fall.

4. Solution Strategy: We check each domino and calculate how many stones fall if it is pushed in either direction.

Upon reviewing the question details and calculations, the correct answer appears to be 1, RIGHT, 4.

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Задание 6 (Question 6)

Question:
We need to apply the bitwise OR (|) operation to the numbers 15 and 7.

1. Convert numbers to binary:

   • $15_{10} = 1111_2$
   • $7_{10} = 0111_2$

2. Apply bitwise OR (|):

   text
   1111
   0111
   ----
   1111

3. Convert back to decimal:

   • $1111_2 = 15_{10}$

Correct answer: 15

Задание 8 (Question 8)

The task is about identifying which algorithm outputs the elements below the main diagonal of a square matrix, based on the flowchart provided.

Let’s break down the flowcharts:

1. First Flowchart (Algorithm 1):

   • This algorithm seems to work on the rows and columns, and it would visit elements below the main diagonal, which are the elements where row index $i$ is greater than column index $j$.

2. Second Flowchart (Algorithm 2):

   • This one works similarly but seems to cover the main diagonal itself as well. It doesn’t focus solely on elements below the diagonal.

3. Third Flowchart (Algorithm 3):

   • This algorithm focuses on visiting all elements below the main diagonal by incrementing the row and column appropriately. It outputs elements strictly below the diagonal.

4. Fourth Flowchart (Algorithm 4):

   • This one checks all elements including the diagonal, so it wouldn't fit the task.

Answer: The correct algorithms are 1 and 3, as they output elements below the main diagonal.

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Задание 9 (Question 9)

We need to evaluate the following set operation:

Where:

• $A = \{1, a, b\}$
• $B = \{c, d, e\}$
• $C = \{5, a, b\}$
• $U = \{1, 2, 3, 4, 5, a, b, c, d, e\}$

Step-by-Step Solution:

1. Find $B \cup C$ (Union of B and C):

   $$B \cup C = \{c, d, e\} \cup \{5, a, b\} = \{c, d, e, 5, a, b\}$$

2. Find $A \cap (B \cup C)$ (Intersection of A and $B \cup C$):

   $$A \cap (B \cup C) = \{1, a, b\} \cap \{c, d, e, 5, a, b\} = \{a, b\}$$

Answer: {a, b}

The correct option is (a,b,c,e).

Let me know if you'd like further clarification!