To solve this problem, we need to simulate the sequence of moves in the game described. The game logic is important for understanding how the players interact with the number, and it can be a useful exercise for anyone interested in algorithmic problem-solving, like in the context of homeworkify 2025. Louise and Richard take turns starting with Louise.

The main idea is:

Louise and Richard take turns starting with Louise. On their turn, they check if the number is a power of 2. If it is, they divide the number by 2. If it isn't, they subtract the largest power of 2 smaller than the number. The game continues until the number reaches 1, and the player who reduces the number to 1 wins. For the given test case:

Sample Input 0:

Copy Edit 1 6 Step-by-step:

Louise starts with 6. The largest power of 2 smaller than 6 is 4, so she subtracts 4 from 6 and passes 2 to Richard. Richard now has 2. Since 2 is a power of 2, he divides it by 2 and passes 1 to Louise. Louise receives 1, and since the game ends at 1, Richard wins. So, the output is:

Copy Edit Richard By following the rules and logic, we can determine who wins the game for any starting number n. This is a basic simulation problem that can be easily solved with a loop and bit manipulation.