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Answer:

Use prime factors to eliminate possibilities:

Her name = 10x21x4x7x5

She can’t have a U(21), or a G(7), no it must have 2 N(14)

She can’t name an E(5), or a J(10), and can’t have an O(15) because that would mean she would need an E or a J.  So her name has a y(25).

This leaves 2x3.  Since she can’t have a C, she must have an F.  The last factor is a 1, which means A.

The Judge’s wife’s name is ‘Fanny’

 
 
Here Come the Judge

The judge is a numerologist.

Using a=1, b=2, etc,

   1. His wife has a name whose product is the same as that of “JUDGE”
   2. His wife’s name has no letter in common with “JUDGE”
   3. His wife’s name does not contain a “C”
   4. When the first and second letter are interchanged, his wife’s name’s letters are arranged alphabetically.

What is the name of the Judge’s wife?