Fill as much of a 6x6 grid with the letters A, B, C, D, E, F so no two of the same letter are in the same row, column or diagonal.

It is impossible to entirely fill the grid, but what is the largest number of letters that may be placed?

The program finished and found nothing better than 33 valid placements.  The limitation of the program is that it counts out positions that conflict on the diagonal, while allowing their initial placement.  I don't know if it would affect things if diagonal placement were primary and orthogonal conflicts flagged.

The last few found (by changing < to <= when comparing conflict count to the best so far) are:

 3
adbfce
becdaf
cafbed
dbEAfc
efdcba
fcaedB

 3
adbfce
becdaf
cafbed
dbAEfc
efdcba
fceadB

 3
adbfce
bAcdEf
cefbad
dbaefc
efdcba
fceadB

 3
acebfd
bfacDe
cedfba
dbcAef
eafdcb
fdbeaC

 3
acebfd
bdfcae
ceADbf
dbcfea
efdacb
fabedC

 3
acebfd
bAfcDe
cedabf
dbcfea
efadcb
fdbeaC

Posted by Charlie on 2006-05-23 10:24:14