Chandra, Dressed to Kill

[+1]: Add {R}. Chandra, Dressed to Kill deals 1 damage to up to one target player or planeswalker.
[+1]: Exile the top card of your library. If it's red, you may cast it this turn.
[−7]: Exile the top five cards of your library. You may cast red spells from among them this turn. You get an emblem with "Whenever you cast a red spell, this emblem deals X damage to any target, where X is the amount of mana spent to cast that spell."

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Chandra's first ability uses the stack and can be responded to, even if no targets were chosen. It doesn't count as a mana ability.

Chandra's last ability, by contrast, only allows you to cast spells that are red when you cast them, no matter what the card in exile is. If Rowan, Scholar of Sparks is exiled by this ability, you won't be able to cast Will, Scholar of Frost this way because it would be a blue spell.

Chandra's second ability checks the characteristics of the card you exiled to see if it's red. If the spell that card becomes somehow isn't red, you may still cast it. For example, Rowan, Scholar of Sparks, the front face of a modal double-faced card, is red. Will, Scholar of Frost, the back face of the same card, is blue. In exile, that card is red, so you may cast either face if you exile it with this ability.

The emblem's triggered ability looks for the actual amount of mana spent to cast the spell. If an effect caused you to pay more or less mana for that spell as you cast it, that will be taken into account when determining the value of X. If an effect would counter that spell unless you pay some amount of mana, that mana doesn't count as mana spent to cast it.

You must pay all costs for spells cast via Chandra's last two abilities. For the middle ability, you must also follow all timing restrictions.