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No way to run a railroad. (Posted on 2010-10-01) Difficulty: 3 of 5

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.

No Solution Yet Submitted by broll    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(2): extra creditbroll2010-10-03 04:30:19
re: extra creditDaniel2010-10-02 21:07:19
extra creditbroll2010-10-02 15:32:48
extra creditDaniel2010-10-02 12:07:02
computer solutionDaniel2010-10-02 11:43:01
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