How does methyl vinyl ketone dimerise with heating? (A) to (B) is simply reduction, tosylation followed by intramolecular reaction and removal of tosylate. However, I am not able to guess how dimerization will take place, seems similar to Rauhut–Currier reaction, but can't guess. Any hint?
The dimer of methyl vinyl ketone (1) is not shown in the choices in the question. The dimer is A shown below. It is a "tail-to-tail" dimer. Product B is an intramolecular ketal as a probable mixture of epimers. Compare with this paper. 



B. P. Mundy, et al., J. Org. Chem., 1978, 43, 2347.