Question

Чебурашка записал на доске некоторое число, используя цифры 2,3,4. Оказалось, что в этом числе цифра 2 встречается хотя бы один раз среди любых двух соседних, цифра 3 встречается хотя бы один раз среди любых трех соседних. В выписанном на доске числе встречается две четверки и 10 двоек. Сколько троек может быть в записи этого числа?

Answer 1

Четыре, так как 12 разделить на 3 равно 4

Answer 2

Analysis and Solution

To determine the number of occurrences of the digit 3 in the given number, we need to analyze the conditions provided.

The conditions state that the digit 2 appears at least once among any two adjacent digits, and the digit 3 appears at least once among any three adjacent digits. Additionally, the number contains two 4s and ten 2s.

Let's break down the problem step by step:

1. The number contains two 4s. This means that the number must have at least two digits that are equal to 4.

2. The number contains ten 2s. This means that the number must have at least ten digits that are equal to 2.

3. The digit 2 appears at least once among any two adjacent digits. This means that there must be at least one occurrence of the digit 2 between any two adjacent digits in the number.

4. The digit 3 appears at least once among any three adjacent digits. This means that there must be at least one occurrence of the digit 3 between any three adjacent digits in the number.

Based on these conditions, we can conclude that the number must have at least 12 digits in total (two 4s and ten 2s). Additionally, there must be at least one occurrence of the digit 2 between any two adjacent digits and at least one occurrence of the digit 3 between any three adjacent digits.

Now, let's determine the maximum number of occurrences of the digit 3 in the number.

To maximize the number of occurrences of the digit 3, we can place a 3 between every three adjacent digits. Since there are twelve 2s in the number, we can place a 3 between every three pairs of adjacent 2s. This would result in a total of four occurrences of the digit 3 in the number.

Therefore, the maximum number of occurrences of the digit 3 in the given number is four.

Please let me know if anything is unclear or if you need further assistance!