55. Roller Calibration. One of the components of a gasoline engine has the shape of a roller. To measure the thickness of the roller, a steel plate is used, in which 15 holes are drilled in a row with precisely established dimensions. The first hole has a diameter of 10 mm, and each subsequent hole has a diameter 0.04 mm larger than the previous one. The calibration of the roller involves inserting it into the hole; if it does not fit, its diameter is considered larger than the diameter of the hole, and if it fits, it is considered smaller. Thus, in the end, the diameter of the roller is determined with an error of less than 0.04 mm (rollers with a diameter less than 10 mm or more than 10.56 mm are not considered; the rest are processed further).

Workers assigned to calibration try each roller on the same number of holes, but, of course, on different holes. How many measurement trials are necessary for each roller? What should be the order of the trials?
55. In any case, four trials are sufficient if the following method is adopted: we will compare the roller with the average hole, i.e., the eighth in order, then, depending on the result, with the fourth or twelfth, and so on. The result of each trial will be an answer "Yes" (if the roller fits into the hole) or "No" (if the roller does not fit into the hole). Four trials will give 16 possibilities, i.e., as many as there are types of rollers distinguishable by this device.