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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 exiled cards remain exiled with cage counters when Mairsil leaves the battlefield. If Mairsil returns to the battlefield, it will see all of those exiled cards with cage counters on them.

Activated abilities contain a colon. They're generally written "[Cost]: [Effect]." Some keyword abilities (such as equip) are activated abilities and will have colons in their reminder text. Mairsil won't gain triggered abilities (which start with "when," "whenever," or "at").

If an activated ability of a card in exile with a cage counter on it references the card it's printed on by name, treat Mairsil's instance of that ability as though it referenced Mairsil by name instead. For instance, if Mairsil exiles Magus of the Mind, the cost to activate the ability includes sacrificing Mairsil, not sacrificing Magus of the Mind.

If Mairsil has an equip ability, activating it won't cause anything to happen. Mairsil doesn't become attached to a creature. They may remain friends.

If you have a creature enter the battlefield as a copy of Mairsil, its first ability triggers. You won't be able to activate any abilities before the "legend rule" applies, but the triggered ability will still let you exile another card with a cage counter regardless of which Mairsil you keep.

If Mairsil gains an activated ability that's normally linked to another activated ability of the card it came from, those two abilities Mairsil gains are linked for as long as Mairsil remains on the battlefield. For example, if Mairsil exiles Izzet Chemister, cards exiled with the first ability Mairsil gained from Izzet Chemister can be cast if you activate the second ability it gained that way. Izzet Chemister itself can't be cast this way, and if Mairsil leaves the battlefield before activating that second ability, the cards exiled with that first ability are lost forever.

If multiple cards exiled with cage counters on them have the same ability, Mairsil will have multiple instances of that ability. Each may be activated once each turn.

If another player gains control of Mairsil, it will have the abilities of only cards that player owns in exile with cage counters on them.

If Mairsil gains an activated ability that's normally linked to a non-activated ability of the card it came from, the ability Mairsil has isn't linked to any ability. For example, if Mairsil exiles Prototype Portal, the activated ability creates no tokens at all; it doesn't create Prototype Portal tokens.

If one of Mairsil's abilities doesn't resolve, most likely because its target became illegal before it resolved, it can't be activated again in the same turn.

If Mairsil has a crew ability, creatures can crew Mairsil. It'll become an artifact creature, but its power and toughness remain unchanged.