Problem 1. Recall that in our initial analysis and mapping, we concluded that we were going to need one of the several related base-promoted condensation reactions. Further, we concluded that the methyl next to the side-chain carbonyl ultimately needed to become attached to the six-ring carbonyl, and the aldehyde function would be lost along with a molecule of water. Here is a mechanism that accomplishes those transformations (thanks to Ahmed Malkawi for providing the graphic).

In step (2), we have not explicitly shown the protonation required to convert the alkoxide to an alcohol; it is most likely accomplished by abstraction of a proton from a water molecule. Methanol also is a possible source, but is less acidic.

The dehydration in step (3) is facilitated by the formation of a conjugated enone. In step (5), the decarboxylation is analogous to the behavior of a b-keto acid; in this case, we have a vinylogous b-keto acid. That is, the carboxyl is conjugated to the carbonyl, instead of adjacent.

Problem 2. This problem is made more difficult by the absence of details, such as the solvent and the workup conditions. Most Grignard reactions are conducted in ether, and worked up by treatment with dilute acid, so may may assume that that is the case here. Another problem is that only 65% of the products are specified. Often minor products can give us a clue as to how the reaction proceeds. Here is a fairly speculative methanism:

The 27% product is that expected for normal conjugate addition. While it is known that Grignard addition to carbonyls involves a complex of the Grignard with the carbonyl oxygen, no evidence is available regarding the involvement of such a complex in conjugate addition. Hence, I have written a simple nucleophilic attack. Protonation of the resulting magnesium alkoxide is presumed to occur during workup.

For the unusual product, I suggest a radical coupling mechanism. Such Wurtz-type coupling typically occurs when either the ketone is hindered, or the Grignard is bulky, thus crowding the transition state for normal addition. I have chosen to add the t-butyl radical at the less hindered end of the double bond, to make a delocalized benzyl radical. This radical must then find a hydrogen atom; I suggest extraction of an H from carbon adjacent to oxygen in the ether solvent.

If this part of the mechanism is correct, we should find products from coupling or disproportionation of two t-butyl radicals: 2,2,3,3-tetramethylbutane, isobutene, and isobutane. These are not mentioned in the source from which I drew this problem.

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