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If I had two Heartless Summonings on the battlefield, and I wanted to play Matter Reshaper, would it be free? Or would he cost one colorless mana. I checked the gatherer for Heartless Summoning for an answer, but it only referred to colored mana.

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Heartless Summoning and similar cost reduction effects like it only reduce the generic component of a mana cost. They do not reduce colorless or colored parts of the cost.

The symbol in Heartless Summoning's ability specifically refers to a generic mana cost, as described in rule 107.4b:

Numerical symbols (such as {1}) and variable symbols (such as {X}) represent generic mana in costs. Generic mana in costs can be paid with any type of mana. For more information about {X}, see rule 107.3.

Rule 117.7 governs cost reduction, and 117.7a in particular covers reducing a cost by an amount of generic mana:

  • 117.7. What a player actually needs to do to pay a cost may be changed or reduced by effects. If the mana component of a cost is reduced to nothing by cost reduction effects, it’s considered to be {0}. Paying a cost changed or reduced by an effect counts as paying the original cost.

    • 117.7a Effects that reduce a cost by an amount of generic mana affect only the generic mana component of that cost. They can’t affect the colored or colorless mana components of that cost.
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In that situation, the total cost of casting Matter Reshaper is {C}, so you would have to pay one colorless mana.

That's because Heartless Summoning's first ability reduces the generic cost of summoning creatures. It doesn't reduce colored costs, colorless costs, or any other costs.

107.4b Numerical symbols (such as {1}) and variable symbols (such as {X}) represent generic mana in costs. Generic mana in costs can be paid with any type of mana. For more information about {X}, see rule 107.3.

117.7a Effects that reduce a cost by an amount of generic mana affect only the generic mana component of that cost. They can’t affect the colored or colorless mana components of that cost.

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