Every competitor in a building competition has to build a continuing structure using 8 unit cubes so that each cube in the structure shares a full face with each of its vertical and horizontal neighbors. There cannot be a hole in the structure, cubes cannot be glued together and you have to be able to climb from the floor to the building one level each step. The score for the building is the product of the base area and the height of the building. At the end of the competition, judges were surprises to see that everyone had a different score. How many competitors could there have been at most at the competition? What was the score of the winning structure?
