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Word Square 5
Recover this BEARish Word Square from the letter location clues.
January 17, 2005
From the introduction, each row and each column of the 5x5 Word Square contains the characters BEAR and a blank cell in some order, so that no character or space can be repeated in a row or a column. By clue 2, A is the 2nd letter down column 2; while by clue 8, A is the 2nd letter across row 2. One of two arrangements must then work: either the A in column 2 is in row 3 and the A in row 2 is in column 3 or the A in column two is the A in row 2. Trying the first possibility, B would be in column 3 of row 3 (clue 6), with the space in row 3 then in column 1. The space in row 2 would then be in column 2 (8). By clue 4, the R in column 1 would be in row 5, and the R in column 4 in row 4, with the space in column 4 in row 5. The B in column 4 would be in row 1 (10). However, there is now no way for an A to fit into column 4--so the first arrangement for clues 2 and 8, that the A in column 2 is in row 3 and the A in row 2 is in column 3, fails. The A in clues 2 and 8 is the same one, in row 2, column 2. There are two possible arrangements for the R's in clue 4: either the R in column 1 is in row 5 and the R in column 4 in row 4, or the R in column 1 is in row 4 and the R in column 4 in row 5. Trying the first arrangement, by clue 10, the B in column 4 would be in row 1. By clue 9, then, the E in row 1 would be in column 3 and the space in column 5. The A in row 1 would be in column 1, with the R in column 2. The E in row 4 would be in column 5 (3). Then the A in row 4 would be in column 3. However, the B would be the 1st letter in row 4, a conflict with clue 1. So, in clue 4, the R in column 1 row 5 and the R in column 4 in row 4 fails; the R in column 1 is in row 4 and the R in column 4 in row 5. The space in column 1 must be in row 5. Since the A in column 2 is the 2nd letter in that column (2), the space in row 1 isn't in column 2. If the space in row 1 were in column 3, the E in row 1 would be the 1st letter down column 4 (9)--no (10). So, the E in row 1 must be in column 3 (9). By clue 10, B is 1st down column 4; so either B is in row 1 or B is in row 2 with a space in row 1. Trying the B in column 4 in row 1, by clue 9, the space in row 1 would be in column 5. The letter in column 2 of row 1 would have to be R, with the A in column 1. By clue 3, the E in row 4 would be in column 5. Then the E in row 5 would be in column 2. By clue 6, the B in column 1 isn't in row 3; it would be in row 2, with the E in column 1 in row 3--a conflict with clue 7. So, in clue 10, the B in column 4 isn't in row 1; it is in row 2, with a space in row 1 of column 4. The E in column 1 can't be in row 3 (7) and must be in row 2. The B in row 3 also can't be in column 1 (6), so the A is; the B in column 1 is in row 1. Then the A in row 1 is in column 5, with the R in column 2. In clue 3, if the E in row 4 were in column 4 and the space in column 5, the A in column 4 would be in row 3, where we already have an A. Therefore, in clue 3, the E in row 4 is in column 5. Then in column 4, the E must be in row 3 with the A in row 4. By elimination, the E in column 2 must be in row 5; and the A in column 3 must be in row 5. B in column 5 then completes row 5. By clue 5, in row 4, the B is in the 2nd column and the space in the 3rd. The space in column 2 is in row 3. In column 3, the B is in row 3 and the R in row 2. Finally, in column 5, the space is in row 2 and the R in row 3. In sum, Word Square 5 is as follows:



 12345
B R E  A
E A R B  
A  B E R
R B  A E
 E A R B

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