From the introduction, each row and each column of the 5x5 Word Square
contains the characters GAME and a blank cell in some order, so that no
character or space can be repeated in a row or a column. By clue 4, M and E
appear in consecutive columns lefttoright in row 1; M and E must therefore
be the first letters in two consecutive columns. By clue 8, G is the 1st
letter in both columns 1 and 3. In clue 4, then, M is in row 1, column 4
and E in row 1, column 5. By clue 1, M is the 4th letter down column 1. If
M were in row 4 with the space in row 5 of column 1, clue 3, where E must be
the 1st letter in row 4, would conflict. So, the M in column 1 is in row 5.
By clue 7, A is the 4th letter in row 2; while by clue 2, A is the 3rd
letter in column 4. The A in row 2 must be in column 5. By clue 5, the M in
column 5 must be in row 3. By clue 8, G is either in row 2 of column 1 and
row 1 of column 3; or G is in row 1 of column 1 and row 2 of column 3.
Trying the first possibility, row 1, column 1 would hold a space and row 1
column 2 an A. Then by clue 3, E would occupy column 1 of row 4, with A in
row 3 of column 1. By clue 2, the A in column 4 would be in row 4. By
elimination, A in column 3 would be in row 5. The space in row 4 would be in
column 2 (clue 9). By clue 6, E in row 2 would be in column 2 with the space
in column 4 and the M in column 3. However, there is now no way for M to fit
in column 2. Therefore, the first possibility fails, and G is in row 1 of
column 1 and row 2 of column 3. The space in row 1 is in column 3, with the
A in column 2 of the row. The A in column 1 cannot be the 1st letter in row
4 (3) and is in row 3. By clue 2, A is in row 4 of column 4; by elimination,
the A in column 3 is in row 5. If the E starting row 4 were in column 2
with the space in column 1 (9), the G in row 4 would be in column 5 and the
M in row 4 in column 3. The column 5 space would be in row 5. Then the
row 5 E would be in column 4 and the row 5 G in column 2no (10). So, the
E in row 4 is in column 1 (3) with the space in column 2 (9). The space in
column 1 is in row 2. The G in row 4 is in column 5, with the M in column
3 of the row. Then the row 3 E is in column 3. The space in row 5 is in
column 5. In row 2, the M is in column 2 and the E in column 4 (6). The row
5 E is in column 2, so that G is in column 4 of that row. Finally, row 4,
column 2 contains G; and row 3 column 4 contains space. In sum, Word
Square 4 is as follows:
 1  2  3  4  5 
1  G  A   M  E 
2   M  G  E  A 
3  A  G  E   M 
4  E   M  A  G 
5  M  E  A  G  


