A certain computer program reorders the letters of any seven-letter se

 


The question says that the position of a letter in the new order depends only on its position in the original order. Then we are told that ABCDEFG was reordered to DABCGEF.

ABCDEFG
DABCGEF

Observe that in the first four letters, ABCD, the change was that the first three letters and the fourth letters were switched: ABCD became DABC. In the last three letters, EFG, the first two letters and the third letter were switched: EFG became GEF.

Hence, the first four letters would change the following way:

ABCD - The initial order

1. DABC
2. CDAB
3. BCDA
4. ABCD - Back to the initial order

The last three letters would change the following way:

EFG - The initial order.

1. GEF
2. FGE
3. EFG - Back to the initial order

As we can see, the first four letters cycle back to the initial order after every 4 runs and the last three letters cycle back to the initial order after every 3 runs. Therefore, the entire word will cycle back to the initial order of ABCDEFG in 12 runs:

ABCD - EFG - The initial order

1. DABC - GEF
2. CDAB - FGE
3. BCDA - EFG
4. ABCD - GEF
5. DABC - FGE
6. CDAB - EFG
7. BCDA - GEF
8. ABCD - FGE
9. DABC - EFG
10. CDAB - GEF
11. BCDA - FGE
12. ABCD - EFG - Back to the initial order

Answer: C.­­­­­