ABC and ABCD grid fill-in puzzles

The following puzzle appeared in the Singapore Airlines in-flight magazine.
B

CA
A

B
C

Enter in each row and column the letters A, B and C in such a way that no row or column contains the same letter twice. Therefore two squares in each row or column remain empty. The letters outside the grid indicate what letter is to be entered first in the direction of the arrow.

Here's another such puzzle which I constructed. Instead of a 5x5 ABC puzzle, this one is a 6x6 ABCD puzzle.

B

A
D
DC
A

D C

Here is a step-by-step solution for this second puzzle.
B

 4 7 1 5 6 2 6 5 3 8

A
D
DC
A

D C

• 1 -- This cell cannot be 'D' ('D' is bottom-most in that column, but no room for A,B,C above it), nor any other letter ('D' is leftmost in row) so is empty.
• 2 -- This cell cannot be 'D' ('D' bottom-most in column and, with 1 empty, no room for A,B,C above), nor any other letter, so is empty.
• 3 -- This cell is 'D'. (Both empty cells in column located.)
• 4 -- This cell is 'A'. (Right-side A hints exclude other possibilities).)
• Two 'D's are at either 5 & 5 or at 6 & 6 ('D' in these rows cannot be further right and still leave room for A,B,C).
• 7 -- This cell is 'D' (no other place for 'D' in rightmost column).
• 8 -- This cell is 'A' (no other place for 'A' in 2nd column).
B

 A D 9 10 11 12 12 11 13 10 9 D A

A
D
DC
A

D C
• The 2nd and 5th-row D's are either at 9 & 9 or at 10 & 10. In either case, the 'A' in those rows are in rightmost two columns.
• The 3rd and 4th-row A's are either at 11 & 11 or at 12 & 12 (only ways to put A's in those columns).
• With D's and A's dictated in 3rd- and 4th rows as above, the B's and C's for those rows are somewhere in rightmost three columns.
• 13 -- must be 'B' (only possibility in that row). This forces a 'C' to its right.
B

 A D 15 B C D A 14

A
D
DC
A

D C
• 14 -- This cell is 'B' (only place for 'B' in bottom row).
• 15 -- This cell is 'B' (only place for 'B' in 3rd row).
• Using previous observations, the D's and A's in 3rd and 4th rows are now forced.
B

 A D D A B D A B C 17 16 D A B

A
D
DC
A

D C
• 16 -- This cell is 'D' (topmost cells in 4th column must be empty, 'D' in bottom row is taken elsewhere). The cell below 16 is 'C'.
• 17 -- This cell is 'C'.
• The 3rd row is readily forced, follow by 1st column, 2nd column, 3rd column, and remaining cells.
Summary:
B

 A C B D C B D A D A B C D A B C B C D A D A C B

A
D
DC
A

D C