Button may be a verb, but it doesn't have to. Generally, buttons represent one of three things:

1. an action – this is usually a verb in the imperative mood (e.g. Reply, Save, Add to basket)

2. a status – those omit the verb and only specify the new state of an object, which might be a lot of things, like a noun (Spam), an adjective (Favourite) or maybe an adverb (In progress, Later)

3. a navigation item – on the Web, this is better represented as a link, so let's not go into this here

I would argue that "with/without sound" is a clear example of a status here.

I think most people would agree your solution is preferable, but the spirit of this subthread was "what's the smallest change that would improve things" rather than "how could it be redesigned from scratch?"

I would also argue the MathDoku problem is different. That sounds like a mode confusion type issue, where the user expects a certain level of automation but it has been disabled by the system without adequate feedback.