BYE-LAWS of the H.PIPER STEAM-ENGINE RAILROAD (H.P.S-E.R.R.)
1. Every train on the H.P.S-E.R.R. must comprise only consecutively serial-numbered wagons.
2. Once chosen, such wagons must be assembled in ascending order of the quantity, size and (if necessary) power of the distinct prime factors of the wagons’ serial-numbers; e.g car 41 before car 1681(41,41) before car 39(3,13 )before car 30(2,3,5).
3. The lowest serial-numbered wagon must be in caboose* position.
If the serial-number of the first wagon in today's train is a perfect cube, what is the maximum length of the train?
(Small hint: wagon No. 194481 is the most recent addition to the rolling stock of the H.P.S-E.R.R.)
There is also a bonus, for the ingenious reader.
* a 'caboose' is the last wagon at the back end of the train.