Solving puzzles does not directly alter genetics any more than a giraffe stretching his neck up alters the genetics of his neck.
However, solving more puzzles (which in evolutionary terms, means figuring out how to get food better, and how to get more mates better) does indirectly benefit intelligence as expressed genetically the same way any other feature evolving does.
Furthermore, learning involves physical changes to the brain, and there's plenty of evidence for "use it or lose it" in terms of any particular individual's brain and ability to think. Of course, this mechanism, like exercise builds muscles, also evolved.
Of course, an interesting phenomenon is under way, though it may be hundreds of years before it expresses itself. Intelligence has grown so much that it has taken on the ability to care for other, less intelligent people. Now given genetics is constantly re-rolling the dice on everyone every generation, some people are a little smarter, others a little dumber. The evolutionary pressure on dumbness that was so useful to hew away an intelligent human over the eons now no longer functions -- dumb people aren't starving to death. Hence, while the average intelligence may not change much, smarter and dumber people will continue to evolve, with the dumber not being culled
because of the existence of the smarter people. Throw into the mix the knowledge that the more earning power people have, the fewer children they have, and the "dumbo bulb" of people may grow even larger, skewing average intelligence.
Of course, there are a million things besides (lack of) intelligence no longer being culled evolutionarily thanks to intelligence. No escape for humanity? Of course there is!
Long before humanity devolves into a handful of super-geniuses and a bunch of lazy blobs a dumb as a bag of hammers, the super-intelligent will boostrap away from genetics. The
transhumanist Omega point is almost here!
(ducks and runs)