The bases A through E are odd and balanced. Base X is unbalanced and equal to the sum of the odd bases.
(???)X = (1!!1011!1)A
(???)X = (00020!002)B
(???)X = (00002#!@2)C
(???)X = (000003322)D
(???)X = (00001#5%4)E
For those of you who are not familiar with balanced number systems, Wikipedia provides a good overview. I also recommend taking a look at these Tri-Valley based puzzles; GC8Z7ZJ, GC8ZNGB, and GC94585. These all use the balanced ternary number system in interesting ways.
Congratulations to first finder Dr. Flonase.
