Invariant reactions can be told apart by looking at the phases present before and after the reaction: whether they involve a liquid, and how many solid phases combine or split. Let's check the given reaction, \( \text{Solid 1} + \text{Solid 2} \rightarrow \text{Solid 3} \), against each option.
- Eutectic reaction: This reaction starts from a single liquid phase and produces two solid phases on cooling, \( \text{Liquid} \rightarrow \text{Solid 1} + \text{Solid 2} \). The given reaction starts from two solids, not a liquid, so it cannot be eutectic.
- Peritectic reaction: This involves a liquid combining with an existing solid to form a new solid, \( \text{Liquid} + \text{Solid 1} \rightarrow \text{Solid 2} \). Again, a liquid phase is required, which is absent from the given reaction.
- Eutectoid reaction: This is the solid-state analogue of the eutectic reaction, where one solid phase splits into two different solids on cooling, \( \text{Solid} \rightarrow \text{Solid 1} + \text{Solid 2} \). This is the reverse direction of what's given (splitting, not combining), so it does not match.
- Peritectoid reaction: This is the solid-state analogue of the peritectic reaction, where two existing solid phases combine on cooling to form a third, new solid phase, \( \text{Solid 1} + \text{Solid 2} \rightarrow \text{Solid 3} \). This matches the given reaction exactly, both in that everything is solid-state and in the direction of combination.
Only the peritectoid reaction has two solids combining into a third with no liquid phase involved anywhere, matching the given transformation exactly.
Therefore, the correct answer is Peritectoid reaction.