Question

Пентагон случайно узнал, что пароль от страницы Василия Коровкина в соц сети- это пятизначное,не кратное пяти число,у которого на чётных местах стоят нечётные цифры. сколько времени займёт у Пентагона взлом аккаунта Васи, если супер-компьютер Пентагона перебирает разные варианты со скоростью 1 пароль в секунду???

Answer 1

Последнее число не может быть 0 или 5 (пароль не кратен пяти). Значит последних цифр возможно 8 вариантов.

2 и 4 цифры - нечетные цифры (которых 5). Значит 2 и 4 цифры всего по 5 вариантов.

Первой и третьей цифры - по 10 вариантов (от 0 до 9). Значит всего вариантов пароля:

10*5*10*5*8=20000 вариантов.

Значит взлом пароля займет 20000 секунд или 20000/3600=5часов33минуты20секунд - ответ

Answer 2

The Pentagon's Password Dilemma

The Pentagon accidentally discovered that the password for Vasily Korovkin's social media page is a five-digit number that is not divisible by five, with odd digits in even positions. The question is, how long will it take for the Pentagon's supercomputer to crack Vasily's account if it tries different password combinations at a rate of one password per second?

To solve this problem, we need to determine the number of possible passwords that meet the given criteria and then calculate the time it would take to try all those combinations at a rate of one password per second.

Determining the Number of Possible Passwords

To find the number of possible passwords, we need to consider the conditions given: - The password is a five-digit number. - The number is not divisible by five. - Odd digits are in even positions.

Let's break down the conditions step by step:

1. The password is a five-digit number: This means the password can have any digit from 0 to 9 in each position. Since repetition is allowed, there are 10 options for each digit position.

2. The number is not divisible by five: To find the number of five-digit numbers that are not divisible by five, we need to subtract the number of five-digit numbers that are divisible by five from the total number of five-digit numbers.

The total number of five-digit numbers is calculated as follows: - The first digit can be any digit from 1 to 9 (9 options, as 0 cannot be the first digit). - The remaining four digits can be any digit from 0 to 9 (10 options each). - So, the total number of five-digit numbers is 9 * 10 * 10 * 10 * 10 = 90,000.

The number of five-digit numbers that are divisible by five can be calculated as follows: - The last digit must be either 0 or 5 (2 options). - The remaining four digits can be any digit from 0 to 9 (10 options each). - So, the number of five-digit numbers divisible by five is 2 * 10 * 10 * 10 * 10 = 20,000.

Therefore, the number of five-digit numbers that are not divisible by five is 90,000 - 20,000 = 70,000.

3. Odd digits are in even positions: This condition means that the odd digits (1, 3, 5, 7, 9) can only be in the second and fourth positions.

- The second position can have any odd digit (5 options). - The fourth position can also have any odd digit (5 options).

Therefore, the number of possible passwords that meet all the given conditions is 5 * 10 * 5 * 10 * 5 = 12,500.

Calculating the Time Required to Crack the Password

Now that we know there are 12,500 possible passwords, we can calculate the time it would take for the Pentagon's supercomputer to try all these combinations at a rate of one password per second.

Since there are 12,500 possible passwords and the supercomputer tries one password per second, it would take 12,500 seconds to try all the combinations.

Converting this to minutes and hours: - 12,500 seconds ÷ 60 seconds/minute = 208.33 minutes (rounded to the nearest minute). - 208.33 minutes ÷ 60 minutes/hour = 3.47 hours (rounded to the nearest hour).

Therefore, it would take approximately 3 hours and 28 minutes for the Pentagon's supercomputer to crack Vasily's account if it tries different password combinations at a rate of one password per second.

Please note that this calculation assumes the supercomputer can try passwords in a sequential manner without any optimization techniques. In reality, advanced algorithms and techniques can significantly reduce the time required to crack passwords.