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Adric, Mathematical Genius's first ability targets an activated or triggered ability that is on the stack and creates another instance of that ability on the stack. It doesn't cause any object to gain an ability.

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The source of the copy from Adric, Mathematical Genius's first ability is the same as the source of the original ability.

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Activated abilities contain a colon. They're generally written "[Cost]: [Effect]." Some keyword abilities (such as equip) are activated abilities and will have a colon in their reminder text.

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Triggered abilities use the word "when," "whenever," or "at." They're often written as "[Trigger condition], [effect]." Some keywords (such as prowess) are triggered abilities and will use "when," "whenever," or "at" in their reminder text.

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If an ability is linked to a second ability, copies of that first ability are also linked to that second ability. If the second ability refers to "the exiled card," it refers to all cards exiled by the first ability and the copy. For example, if Fiend Hunter's enters-the-battlefield ability is copied and two creatures are exiled, they both return when Fiend Hunter leaves the battlefield.

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Adric, Mathematical Genius can copy any activated or triggered ability on the stack, not just one with targets.

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The copy is created on the stack, so it's not "activated." Creating the copy won't cause abilities that trigger when a player activates an ability to trigger. Abilities that say that a triggered ability triggers additional times won't apply to copying a triggered ability.

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The copy will resolve before the original ability does.

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The copy will have the same targets as the ability it's copying unless you choose new ones. You may change any number of the targets, including all of them or none of them. If, for one of the targets, you can't choose a new legal target, then it remains unchanged (even if the current target is illegal).

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If the ability that's copied is modal (that is, it says "Choose one —" or the like), the copy will have the same mode. A different mode can't be chosen.

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If the ability that's copied has an X whose value was determined as it was activated, the copy will have the same value of X.

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If the ability has damage divided as it was put onto the stack, the division can't be changed, although the targets receiving that damage still can. The same is true of abilities that distribute counters.

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You can't choose to pay any activation costs for the copy. However, effects based on those costs that were paid for the original ability are copied as though those same costs were paid for the copy.

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Any choices made when the ability resolves won't have been made yet when it's copied. Any such choices will be made separately when the copy resolves. Most notably, if a triggered ability asks its controller to pay a cost, you pay that cost for the copy if you wish to have it paid.

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The Doctor's companion ability allows you to have two commanders if one has the ability and the other is a legendary creature that is a Time Lord Doctor and has no other creature types. Creatures with the changeling ability, for example, can't be a second commander this way.

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Although Doctor's companion is a new variant of the partner ability, the rules for partner have not otherwise changed. Notably, Time Lord Doctors and cards with Doctor's companion do not interact with cards which have another partner ability.

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If your Commander deck has two commanders, you can include only cards whose own color identities are also found in your commanders' combined color identities.

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Both commanders start in the command zone, and the remaining 98 cards (or 58 cards in a Commander Draft game) of your deck are shuffled to become your library.

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Once the game begins, your two commanders are tracked separately. If you cast one, you won't have to pay an additional the first time you cast the other. A player loses the game after having been dealt 21 combat damage from any one of them, not from both of them combined.

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If something refers to your commander while you have two commanders, it refers to one of them of your choice. If you are instructed to perform an action on your commander (e.g. put it from the command zone into your hand due to Command Beacon), you choose one of your commanders at the time the effect happens.