Coding Logic Explained

The question presents a substitution cipher where the word 'LOCAT' is coded as 'MQFEY'. We need to determine the pattern used and apply it to the word 'GRAPH'.

Let's compare the letters of 'LOCAT' and 'MQFEY' position by position:

• 1st letter: L (12th) -> M (13th). Difference is +1.
• 2nd letter: O (15th) -> Q (17th). Difference is +2.
• 3rd letter: C (3rd) -> F (6th). Difference is +3.
• 4th letter: A (1st) -> E (5th). Difference is +4.
• 5th letter: T (20th) -> Y (25th). Difference is +5.

The pattern is that each letter in the original word is shifted forward in the alphabet by a number corresponding to its position in the word. The shift increases by one for each subsequent letter.

Applying the Pattern to GRAPH

Now, we apply this identified pattern to the word 'GRAPH':

• 1st letter (G): Position + 1. G is the 7th letter.
  Calculation: $7 + 1 = 8$. The 8th letter is H.
• 2nd letter (R): Position + 2. R is the 18th letter.
  Calculation: $18 + 2 = 20$. The 20th letter is T.
• 3rd letter (A): Position + 3. A is the 1st letter.
  Calculation: $1 + 3 = 4$. The 4th letter is D.
• 4th letter (P): Position + 4. P is the 16th letter.
  Calculation: $16 + 4 = 20$. The 20th letter is T.
• 5th letter (H): Position + 5. H is the 8th letter.
  Calculation: $8 + 5 = 13$. The 13th letter is M.

Combining these results, the word 'GRAPH' is written as 'HTDTM' in the given code.

Final Answer

The coded word for 'GRAPH' is HTDTM.