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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The ability can be activated if the opponent has no lands that produce mana, but the effect will not be able to generate any mana.

It only produces one mana even if the land can produce more than one.

This works even if the opponent's lands are tapped. It only checks what kinds of mana can be produced, not if the abilities that produce them are usable right now.

Fellwar Stone doesn't care about any restrictions or riders your opponents' lands (such as Ancient Ziggurat or Hall of the Bandit Lord) put on the mana they produce. It just cares about colors of mana.

Fellwar Stone checks the effects of all mana-producing abilities of lands your opponents control, but it doesn't check their costs. For example, Vivid Crag has the ability "{T}, Remove a charge counter from Vivid Crag: Add one mana of any color." If an opponent controls Vivid Crag and you control Fellwar Stone, you can tap Fellwar Stone for any color of mana. It doesn't matter whether Vivid Crag has a charge counter on it, and it doesn't matter whether it's untapped.

When determining what colors of mana your opponents' lands could produce, take into account any applicable replacement effects that would apply to those lands' mana abilities (such as Contamination's effect, for example). If there is more than one, consider them in any possible order.

The colors of mana are white, blue, black, red, and green. Fellwar Stone can't be tapped for colorless mana, even if a land an opponent controls could produce colorless mana.