Perception Bobblehead
{T}: Add one mana of any color. {3}, {T}: Look at the top X cards of your library, where X is the number of Bobbleheads you control. You may cast a spell with mana value 3 or less from among them without paying its mana cost. Put the rest on the bottom of your library in a random order.
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Official rulings (4) · Scryfall
If a spell you cast has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.
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.
You choose whether to cast a spell from among the cards you’re looking at as Perception Bobblehead’s last ability resolves. You can’t wait to cast one later in the turn. Timing restrictions based on the card’s types are ignored.
The value of X is determined only once, as Perception Bobblehead’s last ability resolves.