I am a relative newbie to AutoCAD; how can I divide a line of given length into equal parts without going through a geometrical solution as I did on 'the board'

Use the DIVIDE command. This command will place points on your line, equally spaced along the length of the line. You just specify how many segments you want. Then just set your Osnaps to snap to Nodes and you will be able to snap to the points.

Many thanks; you are a star!