If the person is inexperienced or does not have a very public profile (no opensource projects), then we will drop back and throw them some random problems to solve but never a puzzle, since most people just memorize the solutions to puzzles or learn the solutions after doing enough interviews.
We prefer giving them problems like writing a text based guess the number game or tic tac toe. Mindless easy to solve project. They could spit it out in the shortest number of lines, which is what the bad puzzle questions encourage, but we are looking for how well the design/architect code. So the person who creates a good class structure and writes tests for his/her game is the one who gets hired, not the person who prefers shortest lines of code.