Mechanism Challenge Answered

Tynchtyk, over at Chemist in a Transition State, posted a very interesting transformation and challenged us to propose a mechanism. Here is the reaction.

At first glance, this looks like some kind of reductive amination reaction. However, on closer inspection, you can see that there is one less carbon in the product than the starting material. Furthermore, there are no reducing agents present, only acid (and presumably water). Of course the obvious starting point is to react the secondary amine with the aldehyde to form a cyclic imminium structure. Once generated, this is nicely set up to undergo a [3,3]-sigmatropic rearrangement to transfer an allyl group to the imminium carbon. The resulting formaldehyde imminium product is then hydrolyzed in the presence of water to afford the product plus an equivalent of formaldehyde. The full mechanism is shown below. Notice I am a stickler for showing every proton transfer step! No shortcuts here.

Tynchtyk says this problem appeared in a science olypiad for High School Students in Moscow. I wish our high school education here in the states was up to this kind of challenge.

Thanks, Tynchtyk, nice problem! In the spirit of problem solving, let me pose a new challenge. This is one of my favorite transformations.