Question

В стране Циферка есть 9 городов с названиями 1, 2, 3, 4, 5, 6, 7, 8, 9. Путешественник заметил, что два города соединены дорогой в том и только в том случае, если из их названий можно составить двузначное число, которое делится на 8. Какое наименьшее количество дорог надо проехать, чтобы попасть из города 7 в город 9?

Answer 1

Ответ:

Для того чтобы двузначное число делилось на 8, необходимо, чтобы последние цифры числа образовывали число, делящееся на 8. Таким образом, города, которые могут быть соединены дорогой, должны иметь следующие номера: 16, 24, 32, 48, 56, 64, 72 и 88.

Из города 7 можно добраться до города 16 по дороге 7-1-6, а затем до города 88 по дороге 16-8-8. Таким образом, минимальное количество дорог, которое необходимо проехать, равно 3. Ответ: 3.

Answer 2

Problem Analysis

In the country of Cifirka, there are 9 cities with the names 1, 2, 3, 4, 5, 6, 7, 8, and 9. The traveler noticed that two cities are connected by a road only if a two-digit number can be formed from their names, which is divisible by 8. The task is to determine the minimum number of roads that need to be traveled to reach city 9 from city 7.

Solution

To find the minimum number of roads to travel from city 7 to city 9, we need to identify the cities that can form a two-digit number divisible by 8 with city 7. We can then check if any of these cities are directly connected to city 9.

Let's analyze the possible two-digit numbers that can be formed from the names of the cities:

- City 1: No two-digit number can be formed with city 7. - City 2: No two-digit number can be formed with city 7. - City 3: No two-digit number can be formed with city 7. - City 4: No two-digit number can be formed with city 7. - City 5: No two-digit number can be formed with city 7. - City 6: No two-digit number can be formed with city 7. - City 7: No two-digit number can be formed with city 7. - City 8: The two-digit number 78 can be formed with city 7. - City 9: No two-digit number can be formed with city 7.

From the analysis, we can see that city 8 is the only city that can form a two-digit number divisible by 8 with city 7. Therefore, to reach city 9 from city 7, we need to travel from city 7 to city 8, and then from city 8 to city 9.

The minimum number of roads that need to be traveled is 2.

Answer

To reach from city 7 to city 9 in the country of Cifirka, the traveler needs to travel through a minimum of 2 roads.

Note: The analysis and solution provided above are based on the given information. If there are any additional constraints or information, please let me know for further assistance.