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 they´re 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 !