Assuming that it has no leading zero, INVENTORY must be the cube of some number between 465 and 999 inclusive, with only one duplicated digit, represented by N in the alphametic. Manual checking suggests that the only such number with those characteristics is 317214568, which is 682^3.
Thus:I=3,N=1,V=7,E=2,T=4,O=5,R=6,Y=8, so that 682 is decoded as RYE.

Posted by broll
on 20110320 02:21:11 