Mechanism for the formation of butanoic acid from ethylacetoacetate My problem sheet asks me: "Draw a mechanism for the formation of $\ce{EtCH2COOH}$ from the reaction of $\ce{MeCOCH(Et)COOEt}$ with $\ce{NaOH}$ in $\ce{EtOH}$"

This has got me stumped. The mechanisms that I have attempted use the hydroxide ion as the base/nucleophile, is this right? My initial thoughts were to make the enolate by deprotonating between the caronyl groups then doing and aldol into the ketone part of another molecule of ethylacetoacetate but this just gives me a complicated molecule that I can't see reacting further. 

I simply cannot find a way to make the product using only the reactants in the question.
I thought about adding solid $\ce{NaOH}$ to ethanol and therefore used $\ce{EtO-}$ ;) :