Logic problems typically challenge you to sort out several individuals (or groups) and several collections of attributes. In the problem shown here, the attributes include the person's name, the number of megapixels in the person's camera, the type of aristocrat the person encountered, and the person's programming language of choice (must have been written by a geek). Clues usually look something like "The PHP programmer is not Jerry or Harley" or "The 5 people were the person with the 5.2-megapixel camera, Jerry, the person who met the archduke, the Flash programmer, and the person with the 7.0-megapixel camera."
You solve logic problems by using a grid in which you can put x's to rule out logically discredited combinations and checkmarks or dots to identify known matches (determined either from provided data or by logical deduction).
In print, logic problems used to come with preformatted grids (created using problem data); I used to buy books full of these problems to keep me busy during long trips. These days, though, I go to Logic-Puzzles.org, which posts dozens of problems, each accompanied by a grid in which a single click places an x, a second click places a dot, and a third click removes all marks. You don't have to register; but if you do, the site will track your achievements (each puzzle is timed, and your score reflects how long you took to solve it).
The ad-supported site is free, courtesy of the Puzzle Baron (the same folks who created WordTwist).