This is a selection of some of the best problems that have been proposed in a number of, so-called, uncommonly difficult I.Q. tests, that appeared over the years on the science fiction magazine OMNI (available at Library Genesis). This collection is not intended to serve as an standardized I.Q. test. Its main goal is to provide both smart amusement and brain training. The 80 questions have been equally divided into two large groups: Verbal Problems and Spatio-Numerical Problems. The diversity of the questions, some quite challenging, has been an intentionally hallmark pursued here.