What route to take in converting ethanol to crotonic acid? The question asks to write the theoretical transformation steps to convert ethanol to crotonic acid in considerable yield. One constraint is that you cannot use any external organic compounds but inorganic catalysts and reagents are allowed and aldol condensation is prohibited. I do not know the answer, but I came up with the following steps:- 


Treatment with $\ce{HBr}$ to form $\ce{CH3CH2Br}$ via $S_N2$.
Treatment with $\ce{Mg}$ in ether, to form corresponding Grignard reagent.
Oxidation of ethanol by Pyridinium chlorochromate to ethanal, and then treating it with the formed Grignard reaction to form $\ce{CH3CHOHCH2CH3}$. 
Acid catalysed dehydration to form $\ce{CH3CH=CHCH3}$.
Using NBS (N-Bromo Succinimide) as an allylic halogenating agent, followed by treatment with aq. $\ce{KOH}$ to give $\ce{CH3CH=CHCH2OH}$.
Oxidising this with PCC followed by Tollen's reagent to selectively oxidise alcohol to acid, to finally yield crotonic acid.


I am unsure if any of these steps are incorrect, i.e if any of these steps will not give appropriate yields of the desired product owing to side reactions. Another problem is that this transformation is too long. Is there any shorter way to carry out this conversion in proper yields?
Allylic bromination and subsequent hydrolysis might be replaced by an allylic oxidation of the butene using selenium dioxide - if that's inorganic enough for you ;)

But I'm wondering whether there's a shorter way. What about the Grignard reaction you described, followed by oxidation (PCC on silica or manganese dioxide) to 2-butenone. Subsequent bromination with bromine in hydrobromic acid should yield an $\alpha,\alpha'$-dibromoketone which, upon treatment with base (Favorskii rearrangement) and, eventually acidic workup should yield crotonic acid.