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 !

 H  E  -  L  P
 E  -  H  P  L
 L  P  E  H  -
 -  L  P  E  H
 P  H  L  -  E

Reasoning:
Defined a space as a dash -
Defined each cell in form x,y where x= row y=column

FROM CLUE 1
H is either 1,1 or 1,2
H not in 1,3 1,4 1,5
1,1 is either H or -

FROM CLUE 2
L is either 3,2 or 4,2
L is not in 1,2 2,2 or 5,2

FROM CLUE 3
E is either 4,4 or 5,4
E is not 1,4 2,4 3,4
4,5 is either E or -

FROM CLUE 4
P is either 2,3 or 2,4
P is not 2,1 2,2 2,5

FROM CLUE 5
H is either 3,4 or 3,5
H is not 3,1 3,2 3,3
3,5 is either H or -

FROM CLUE 6
4,4 isn't a space

FROM CLUE 7
P is either 2,2 or 3,2
P is not 2,2 from 4 therefore P is 3,2
P is not 1,2 4,2 5,2 3,1 3,3 3,4

L is 4,2
L is not 4,1 4,3 4,4 4,5

FROM CLUE 8
4,5 isn't E

FROM CLUE 9
Going through each clue knowing which order each letter appears HELP in original order does not occur in row 2, 3 or 4 and column 2 or 3

FROM CLUE 2 & 7
P and L are 2nd and 3rd letters so 1,2 or 2,2 is -, 5,2 isn't -

assume row 5 spells HELP in order then you get a situation where no colum can spell HELP in order therefore row 1 must spell HELP in order

E is 1,2 or 1,3
L is 1,3 or 1,4
P is 1,4 or 1,5

column 3 & 5 can't spell help in order therefore column 1 spells help in order

L has to be 3,1

3,3 3,4 not L

E is 2,1

2,2 2,3 2,5 not E

H is 1,1

E is 3,3

E nit 1,3 4,3 5,3

1,2 is E

5,2 not E

5,2 is H

5,3 5,5 not H

2,2 is -

2,3 2,4 2,5 not -

4,4 is E

5,5 is E

5,4 is -

1,4 3,4, 5,1 5,3 not -

5,1 is P

4,1 is -

4,3 4,5 not -

3,4 is H

2,4 not H

1,3 is -

1,5 is P

1,4 is L

2,4 is P

3,5 is -

4,5 is H

2,5 is L

2,3 is H

4,3 is P

5,3 is L

Edited on July 7, 2005, 10:06 am

Edited on July 7, 2005, 1:32 pm

Posted by Lisa on 2005-07-07 10:01:50