Each of the letters in bold represents a base ten digit from 0 to 9 to satisfy these alphametic relationships. None of the numbers can contain any leading zero.

               USA is a multiple of UK, and:
               SA is a multiple of K

Determine the respective minimum and maximum values that USA can assume.

(In reply to computer solution by Charlie)

I shall not offer my computer listing since, while it is not exactly the same as Charlie's, it is similarly structured.

There is one significant difference however which allows for an even lower value for USA.  Charlie would get that if his FOR S began with 0 rather than 1.

My table reads:
usa           sa            uk            sa / k
 108           8             12            4
 120           20            15            4
 156           56            12            28
 168           68            12            34
 168           68            14            17
 169           69            13            23
 180           80            12            40
 180           80            15            16
 196           96            14            24
 216           16            24            4
 273           73            21            73
 294           94            21            94
 324           24            36            4
 372           72            31            72
 384           84            32            42
 432           32            48            4
 492           92            41            92

Edited on January 21, 2013, 9:08 pm

Posted by brianjn on 2013-01-21 20:34:32