A company orders in a variety of pieces of metal of lengths:
7cm 17cm 18cm 19cm 25cm 37cm 44cm
46cm 63cm 65cm 82cm 83cm 90cm 100cm
The quality controller, whose task it is to check the length of the incoming parts is correct, has figured out that he can use a straight rod of a particular length, and mark a series of points on it so that all of the lengths in the above list can be measured, either between two of the marks, or from an end to one of the marks. He uses the minimum possible number of marks.
How long is the rod, how many marks were made, and where were they positioned?