Kaya the Inexorable

If the spell has {X} in its mana cost, you must choose 0 as the value of X.

If you cast a spell “without paying its mana cost,” you can’t choose to cast it for any alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, those must be paid to cast the spell.

If you own a face-down card in exile, Kaya’s emblem will let you cast it only if you can look at the card (and only if it’s legendary). If you aren’t allowed to look at the card, you can’t cast it, even if you know it’s legendary.