Question 76
Let $0 \le n \le 5^5$ be an integer. Arrange $n$ black stones and $5^5-n$ white stones in a row, and repeat the following operation 5 times:
Divide the row of stones into groups of 5 stones from left to right. For each group, replace the 5 stones in the group with one stone of the color that appears more frequently among them.
Find the smallest possible value of $n$ for which the single remaining stone at the end is always black regardless of the initial arrangement of stones.
Divide the row of stones into groups of 5 stones from left to right. For each group, replace the 5 stones in the group with one stone of the color that appears more frequently among them.
Find the smallest possible value of $n$ for which the single remaining stone at the end is always black regardless of the initial arrangement of stones.