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Help ! (Posted on 2005-07-07) Difficulty: 2 of 5
Below is a sample 5x5 grid, into which the letters in the word HELP have been written, so that each letter occurs once and only once in each row and column of the grid.
            (1) (2) (3) (4) (5)    
           +---+---+---+---+---+
       (1) | E |   | H | P | L |
           +---+---+---+---+---+
       (2) | P | E | L |   | H |  
           +---+---+---+---+---+
       (3) | H | L | P | E |   |  
           +---+---+---+---+---+
       (4) |   | H | E | L | P | 
           +---+---+---+---+---+
       (5) | H | P |   | L | E |
           +---+---+---+---+---+
Given the clues about letter and space locations that follow, should you be able to HELP rebuild the grid theyīre referring to ?

  1. H is the 1st letter in the sequence across row 1.
  2. The 3rd letter to appear in the order in column 2 is L.
  3. The last letter down column 4 is E.
  4. P is the 3rd letter in the row 2 sequence.
  5. The final letter in row 3 is H.
  6. The space in column 4 isn't in row 4.
  7. P is the 2nd letter down column 2.
  8. The E in row 4 isn't in column 5.
  9. The letters in HELP appear in their original order, though not necessarily consecutively because of the spaces, across one of the rows and down one of the columns.

Note: letter locations are given without regard to the spaces; for example, the 3rd letter in column 1 would mean the letter in either the 3rd or 4th row, depending on where the space is.

Show your reasoning !

  Submitted by pcbouhid    
Rating: 3.3333 (3 votes)
Solution: (Hide)

By clue 4, the letter P is the 3rd letter in the sequence in row 2.

By clue 7, the letter P is the 2nd letter in the order in column 2.

The P in column 2 cannot be in row 2, since that P is in either column 3 or column 4.

So, the P in column 2 is in row 3, with the L in column 2, then in row 4 (clue 2).
            (1) (2) (3) (4) (5)    
           +---+---+---+---+---+
       (1) |   |   |   |   |   |
           +---+---+---+---+---+
       (2) |   |   |   |   |   |  
           +---+---+---+---+---+
       (3) |   | P |   |   |   |  
           +---+---+---+---+---+
       (4) |   | L |   |   |   | 
           +---+---+---+---+---+
       (5) |   |   |   |   |   |
           +---+---+---+---+---+
By clue 1, the H in row 1 must be in column 1 or column 2.

By clue 9, the word HELP is in order in one column, possibly with the space intervening. If this sequence doesn't occur in column 1, but does in 3, 4, or 5, the sequence would have to begin in row 2 - but the L would then conflict with the L in column 2. So, the column in which HELP is in order is column 1, with the H in row 1. Since the L in the sequence can't conflict with the L in column 2, row 4, the L in column 1 is in row 3, and the E is then in row 2 :
            (1) (2) (3) (4) (5)    
           +---+---+---+---+---+
       (1) | H |   |   |   |   |
           +---+---+---+---+---+
       (2) | E |   |   |   |   |  
           +---+---+---+---+---+
       (3) | L | P |   |   |   |  
           +---+---+---+---+---+
       (4) |   | L |   |   |   | 
           +---+---+---+---+---+
       (5) |   |   |   |   |   |
           +---+---+---+---+---+
Similarly, if the word HELP occurs in order, with or without the space in it (clue 9), in row 5, the letter in row 5, column 4 would be L - a conflict with clue 3, which says that the last letter in column 4 is the E. So, the word HELP is in order in row 1.

By clue 5, the 4th letter in row 3 is an H.

In row 3, then, the E can't be in column 5; nor, since the E in column 4 is the 4th letter (clue 3), can the E in row 3 be in column 4. The E in row 3 is in column 3. Then in row 1, the E must be in column 2.
            (1) (2) (3) (4) (5)    
           +---+---+---+---+---+
       (1) | H | E |   |   |   |
           +---+---+---+---+---+
       (2) | E |   |   |   |   |  
           +---+---+---+---+---+
       (3) | L | P | E |   |   |  
           +---+---+---+---+---+
       (4) |   | L |   |   |   | 
           +---+---+---+---+---+
       (5) |   |   |   |   |   |
           +---+---+---+---+---+
Since the L in column 2 is the 3rd letter in that column (clue 2), the H must be in row 5 of column 2, with the space then in row 2.
            (1) (2) (3) (4) (5)    
           +---+---+---+---+---+
       (1) | H | E |   |   |   |
           +---+---+---+---+---+
       (2) | E |   |   |   |   |  
           +---+---+---+---+---+
       (3) | L | P | E |   |   |  
           +---+---+---+---+---+
       (4) |   | L |   |   |   | 
           +---+---+---+---+---+
       (5) |   | H |   |   |   |
           +---+---+---+---+---+
By clue 4, the P in row 2 is in column 4. In row 1, the P in HELP is in column 5.
            (1) (2) (3) (4) (5)    
           +---+---+---+---+---+
       (1) | H | E |   |   | P |
           +---+---+---+---+---+
       (2) | E |   |   | P |   |  
           +---+---+---+---+---+
       (3) | L | P | E |   |   |  
           +---+---+---+---+---+
       (4) |   | L |   |   |   | 
           +---+---+---+---+---+
       (5) |   | H |   |   |   |
           +---+---+---+---+---+
The L in row 1 is then in column 3 or 4. If the L in row 1 were in column 3 and the space in column 4, in row 2, the H would be in column 3 and the L in column 5. The E in column 4 would be in row 5 (clue 3). The H in row 3 would have to be in column 4 (clue 5), since there couldn't be another space in that column. But then the letter in row 4 of column 4 would be an L, conflicting with the L in row 4, column 2. So, the L in row 1 is in column 4 and the space in column 3.
            (1) (2) (3) (4) (5)    
           +---+---+---+---+---+
       (1) | H | E |   | L | P |
           +---+---+---+---+---+
       (2) | E |   |   | P |   |  
           +---+---+---+---+---+
       (3) | L | P | E |   |   |  
           +---+---+---+---+---+
       (4) |   | L |   |   |   | 
           +---+---+---+---+---+
       (5) |   | H |   |   |   |
           +---+---+---+---+---+
In row 2, the L is in column 3 or column 5. If the L were in column 3 and the H in column 5, the H in row 3 would be in column 4 (clue 5) and the space in column 5. The H in column 3 would be in row 4 and the P in row 5. In column 1, the P would be in row 4 and the space in row 5. The L in column 5 would be in row 5, with the E then in row 4. But the space in column 4 would then be in row 4 - no, by clue 6. So, the L in row 2 is in column 5 and the H in column 3. Then the L in column 3 is in row 5, with the P in column 3 in row 4. The P in column 1 is in row 5, with the space in row 4.
            (1) (2) (3) (4) (5)    
           +---+---+---+---+---+
       (1) | H | E |   | L | P |
           +---+---+---+---+---+
       (2) | E |   | H | P | L |  
           +---+---+---+---+---+
       (3) | L | P | E |   |   |  
           +---+---+---+---+---+
       (4) |   | L | P |   |   | 
           +---+---+---+---+---+
       (5) | P | H | L |   |   |
           +---+---+---+---+---+
By clue 8, the E in row 4 is in column 4 and the H in 5. Then the H in row 3 is in column 4 and the space in column 5, and the space in row 5 is in column 4 and the E in column 5.
            (1) (2) (3) (4) (5)    
           +---+---+---+---+---+
       (1) | H | E |   | L | P |
           +---+---+---+---+---+
       (2) | E |   | H | P | L |  
           +---+---+---+---+---+
       (3) | L | P | E | H |   |  
           +---+---+---+---+---+
       (4) |   | L | P | E | H | 
           +---+---+---+---+---+
       (5) | P | H | L |   | E |
           +---+---+---+---+---+

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SampleMath Man2012-09-15 11:09:32
AnswerK Sengupta2009-03-01 04:01:00
SolutionSOLUTION, NO REASONINGscott2005-07-27 12:35:30
SolutionSOLUTION, NO REASONINGscott2005-07-27 12:35:27
re(5): Solution + Reasoning - a questionpcbouhid2005-07-08 15:15:06
re(4): Solution + Reasoning - a questionLisa2005-07-08 09:05:36
re(3): Solution + Reasoning - a questionpcbouhid2005-07-07 14:58:00
re(2): Solution + Reasoning - a questionLisa2005-07-07 12:57:11
re: Solution + Reasoning - a questionpcbouhid2005-07-07 12:47:52
SolutionSolution + ReasoningLisa2005-07-07 10:01:50
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