Question 1210204
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The correct answer is 1074.  How do I know?  I wrote a program in LibertyBasic
to find and count them all.  Here are the first 10 from my output:

1             ABCDBDCDCD
2             ABCDCDBDCD
3             ABCDCDCDBD
4             ABDBCDCDCD
5             ABDBDCDCDC
6             ABDCBDCDCD
7             ABDCDBCDCD
8             ABDCDBDCDC
9             ABDCDCBDCD
10            ABDCDCDBCD

and here are the last 10:

1065          DCDCDBDBAC
1066          DCDCDBDBCA
1067          DCDCDBDCAB
1068          DCDCDBDCBA
1069          DCDCDCABDB
1070          DCDCDCBABD
1071          DCDCDCBADB
1072          DCDCDCBDAB
1073          DCDCDCBDBA
1074          DCDCDCDBAB

Edwin</pre>