Question

Сколько целых чисел от 0 до 99999 не содержат двух цифр 5 подряд в своей десятичной записи?

Answer 1

Если только двух, то 99.996
Если двух и более, то 99.989
(точки можно не писать)

Answer 2

Calculation of Numbers without Two Consecutive 5s

To determine the number of whole numbers from 0 to 99999 that do not contain two consecutive 5s in their decimal representation, we can use a combinatorial approach.

Let's break down the calculation into different cases:

1. Numbers with 0 digits: There is only one number in this case, which is 0.

2. Numbers with 1 digit: There are 10 numbers in this case, from 0 to 9.

3. Numbers with 2 digits: There are 90 numbers in this case, excluding the numbers 55 to 59.

4. Numbers with 3 digits: There are 900 numbers in this case. We can calculate this by multiplying the number of choices for each digit: 9 choices for the first digit (excluding 5), 10 choices for the second digit, and 10 choices for the third digit.

5. Numbers with 4 digits: There are 9000 numbers in this case. Similar to the previous case, we have 9 choices for the first digit, 10 choices for the second, third, and fourth digits.

6. Numbers with 5 digits: There are 90000 numbers in this case, following the same logic as the previous cases.

Adding up the numbers from each case, we get the total number of whole numbers from 0 to 99999 that do not contain two consecutive 5s in their decimal representation.

Total number of numbers without two consecutive 5s: 1 + 10 + 90 + 900 + 9000 + 90000 = 100001

Therefore, there are 100,001 whole numbers from 0 to 99999 that do not contain two consecutive 5s in their decimal representation.