Alisa completes a railway game set which allows us to make various closed railway routes with crossroads. It is need to put the “rails” parts in the kit, as well as four types of “crossroads”: corner (L), through (I), tee (T), central (X). To draw up the route, a dice is used, which is thrown three times. The number of points determines the number of rails that you need to take to compose part of the route. After the first throw, the rails must be connected by crossroads in a straight line, then take the crossroad (L, T or X), which allows you to turn right at a right angle and connect with the rails, the number of which determines the second roll of the die, the rails are connected in the same way after the third roll.
Further, the process will be repeated using the points from 1st step, until the route closes at the original intersection.
What is the minimum number of parts that Alisa needs to put in a set to make a closed route in which all intersections are used to connect the rails?
Question. I need help in checking the uniqueness of the puzzle's statement.