Question

Среди шести цифр которыми записывают трёхзначные числа Α и Α+1 есть ровно три двойки и ровно одна девятка сколько всего чисел Α?

Answer 1

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Answer 2

Number of Possible Values for Α

To determine the number of possible values for Α, we need to find the six-digit numbers that can represent three-digit numbers Α and Α+1, where there are exactly three twos and one nine.

Let's break down the problem step by step:

1. We have six digits to work with, and we need to find the number of ways we can arrange these digits to form a three-digit number Α and Α+1. 2. Since there are three twos and one nine, we can think of the arrangement as follows: 22Α9. 3. The digit Α can take on any value from 0 to 9, excluding 2 and 9, as those are already fixed. 4. Therefore, there are 10 possible values for Α (0-9), minus the two fixed values (2 and 9), resulting in 8 possible values for Α.

So, there are 8 possible values for Α that satisfy the given conditions.