TWO+TWO=NULL
TWO+TWO=ONE
TWO+TWO=FOUR
TWO+TWO=FIVE
TWO+TWO=SIX
TWO+TWO=NINE
Each one of the above mentioned alphametics, treated separately, has more than one base ten solution. Which one has the most? Which one of them, if any, possess an unique solution in another base or bases?

(In reply to computer solution by Charlie)

My base-10 line now agrees with brianjn's. I've gone only to base 23 so as to cut down on processing time.

base  
      NULL   ONE   FOUR   FIVE    SIX   NINE
 5      0      1      0      0      0      0
 6      0      1      0      0      0      0
 7      0      2      1      3      8      0
 8      1      8      5      7     14      5
 9      1     12      5     18     37      7
10      4     17      7     35     64     11
11      6     21     14     72    119     13
12      8     26     20    124    206     26
13     10     42     21    178    264     32
14     14     45     35    275    372     40
15     18     57     39    376    528     41
16     24     73     53    537    702     61
17     28     75     63    657    915     71
18     33     94     72    902   1137     83
19     39    110     80   1097   1409     86
20     46    118    105   1449   1778    114
21     52    142    105   1679   2113    127
22     61    161    127   2106   2494    144
23     69    168    148   2437   3008    145

Six still has the most for base-10.

Unique solutions are for base-5 ONE, base-6 ONE, base-7 FOUR, base-8 NULL and base-9 NULL.

 

Posted by Charlie on 2010-04-12 12:10:17