Comment by cma

I added this line to the end of your prompt so it knew it could clarify and didn't need an immediate answer:

"You can ask any clarifying questions first before starting on the problem."

Here's what it asked (Claude Opus, web search off so it didn't find your post):

> Looking at this problem, I want to make sure I understand the process correctly before diving into the solution. Let me clarify a few things:

> When you say "flip on every fourth one" for the powers of two, do you mean:

> We flip switches at positions 4, 8, 12, 16, 20, 24, ... (every 4th position) Then flip switches at positions 8, 16, 24, 32, 40, 48, ... (every 8th position) And so on?

> When you move to "powers of three", do you mean:

> Start with every 3rd switch (3, 6, 9, 12, ...) Then every 9th switch (9, 18, 27, 36, ...) Then every 27th switch, etc.?

> Or does "powers of three" mean we start with 3² = 9 as the first increment, similar to how we started with 2² = 4 for powers of two?

> When you say "then four, then five, and so on" - do you mean we continue this process for all integers k ≥ 2, using powers of k as our increments?

> The final state of each switch depends on whether it gets flipped an odd or even number of times total, so I want to make sure I understand the flipping pattern correctly before calculating the answer.