| From the introduction, each row and each column of the 5x5 Word Square
contains the characters TIME 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, the
letter I is the 4th letter in order in column 1. If the letter I filled
the 5th cell in column 1, it would fill the 1st cell in row 5; by clue 7,
however, the letter I is the 3rd letter in sequence in row 5. So, the I in
column 1 is in the 4th row, and the 5th row of column 1 has the space. By
clue 7, then, the I in row 5 is in the 4th column. By clue 9, E is the 3rd
letter in row 2, so it will be in column 3 or column 4. If the E in row 2
is in column 3, then the E in column 4 must be in the 1st row (clue 3).
However, there is no way for clue 6, where the E is in the 3rd column of the
4th row, to work given this arrangement. So, the E in row 2 is in column 4,
with the column 4 space then in row 1 (3). The E in row 4 must be in the 3rd
column (6). By clue 2, the T is the 3rd letter in order across row 3, so the
T is in the 3rd or 4th column. If the T were in the 3rd column, by clue 10,
the I would be in row 2 of column 3 and the M in row 1. However, the column 3
space would be in row 5, where there already is the one allowed space. So,
the T in row 3 is in column 4, with the column 4 M in row 4 and the row 3 space
in column 2 or 3. The T in row 4 is in column 2 or column 5. If it were in
column 5, with the space in row 4 in the 2nd column, by clue 1, the E in the
5th column would be in row 3. Since we have a space in rows 1 and 5, then,
the column 5 space would be in row 2, with the M in the 1st row (1) and the
I in the 5th row--where we already have an I. Therefore, the T in row 4 must
be in column 2, with the row 4 space in the 5th column. The space in row 3 is
in column 2 or column 3. If it were in column 3, the row 2 space would be in
column 2. By clue 10, the I in column 3 would be in row 2. If the I in row
3 were in column 5, there would be no way for E to follow M in clue 1, since we
already have an E in row 2. So the I in row 3 would be in column 2. By clue
5, the M in the 3rd row would be in the 5th column, with the E in the 5th
column then in row 5 (1). Filling in according to the Word Square rules,
the I in row 1 would be in column 5, the T in column 5 would be in row 2,
the M in row 2 would be in column 1, and the E in row 3 would be in column 1.
But we now have a conflict with clue 8. Therefore, the space in row 3 is in
column 2, with the row 2 space in the 3rd column. The I in column 3 is in
row 3 (10). By clue 1, the M in column 5 must be in row 2 or row 3. If it
were in row 3 with the E then in row 5 (1), the E in row 3 would be in column
1. By clue 8, the column 1 M would be in row 1 with the column 1 T in row 2.
Then the M in row 2 would be in column 2. We now have a conflict, however.
Row 5, column 2 must contain an M or T, but they are both used in column 2.
So, the M in column 5 must be in row 2, followed by the E in row 3 (1).
The I in column 5 is in the 1st row and the T in column 5 in the 5th row.
The M in row 3 is in column 1, the E in column 1 is in row 1, and the T in
column 1 is in row 2. The I in column 2 is in row 2. The T in row 1 is in
column 3, with the row 1 M in column 2. Finally, the row 5 E is in the 2nd
and the row 5 M in the 3rd column. Word Square 2 is filled as follows:
| | 1 | 2 | 3 | 4 | 5 |
| 1 | E | M | T | | I |
| 2 | T | I | | E | M |
| 3 | M | | I | T | E |
| 4 | I | T | E | M | |
| 5 | | E | M | I | T |
|
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