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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.

Radagast's ability can't reduce the amount of colored mana you pay for a spell. It reduces only the generic component of that cost.

If the first creature spell you cast in a turn has {X} in its mana cost, you choose the value of X before calculating the spell's total cost. For example, if the first creature spell you cast in a turn has a mana cost of {X}{G}, you could choose 2 as the value of X and pay {G} to cast the spell.

Radagast of Rhosgobel's ability will look at the entire turn, even if Radagast wasn't on the battlefield for some of it. Notably, if you cast Radagast of Rhosgobel in a turn, then no other creature spell you cast that turn can be your first.

The cost reduction can apply to alternative costs.

If there are additional costs to cast a spell, or if the cost to cast a spell is increased by an effect, apply those increases before applying cost reductions.

The first creature spell you cast each turn doesn't necessarily have to be the first spell you cast. You could cast a sorcery spell and then cast a creature spell that would get the discount.

Radagast of Rhosgobel's ability doesn't change the mana cost or mana value of any spell. It changes only the total cost you actually pay.