Understanding the Coding Pattern

The question asks us to find the coded word for "PLAY" based on the given example where "GAME" is coded as "ICOG". We need to identify the pattern used to transform "GAME" into "ICOG".

Analyzing the Transformation: GAME to ICOG

Let's examine the relationship between the letters in "GAME" and their corresponding letters in "ICOG". We can look at their positions in the English alphabet:

• G is the 7^th letter. I is the 9^th letter.
• A is the 1^st letter. C is the 3^rd letter.
• M is the 13^th letter. O is the 15^th letter.
• E is the 5^th letter. G is the 7^th letter.

Now, let's find the difference in position for each letter pair:

• I - G = 9 - 7 = 2
• C - A = 3 - 1 = 2
• O - M = 15 - 13 = 2
• G - E = 7 - 5 = 2

The pattern observed is that each letter in the original word is shifted forward by 2 positions in the alphabet to get the corresponding letter in the coded word.

Applying the Pattern to "PLAY"

Using the same pattern (shifting forward by 2 positions), let's find the coded word for "PLAY":

• P: The 16^th letter. Shifting forward by 2 gives the 18^th letter, which is R. ( $16 + 2 = 18 \rightarrow R$ )
• L: The 12^th letter. Shifting forward by 2 gives the 14^th letter, which is N. ( $12 + 2 = 14 \rightarrow N$ )
• A: The 1^st letter. Shifting forward by 2 gives the 3^rd letter, which is C. ( $1 + 2 = 3 \rightarrow C$ )
• Y: The 25^th letter. Shifting forward by 2 gives the 27^th position. Since the alphabet has 26 letters, we wrap around. The 27^th position is the same as the 1^st letter, which is A. ( $25 + 2 = 27 \equiv 1 \pmod{26} \rightarrow A$ )

Combining these letters, the coded word for "PLAY" is "RNCA".

Final Coded Word

Therefore, following the established coding pattern, "PLAY" is written as "RNCA".