Coding-Decoding: Unlocking the Logic of STREAM and PERIOD

This question asks us to decode the word 'PERIOD' based on the coding pattern observed in the word 'STREAM'. The word 'STREAM' is coded as 161418445228. We need to identify the rule applied to each letter.

First, let's list the letters in 'STREAM' and their standard alphabetical positions (A=1, B=2, ... Z=26).

The code given for 'STREAM' is 161418445228. This is a 12-digit number, and 'STREAM' has 6 letters. This suggests that each letter is coded into a 2-digit number. Let's split the code into pairs:

16 | 14 | 18 | 44 | 52 | 28

So, the codes for the letters are:

• S is coded as 16
• T is coded as 14
• R is coded as 18
• E is coded as 44
• A is coded as 52
• M is coded as 28

Now, let's try to find a relationship between the letter's position and its code.

• S (Position 19) → Code 16
• T (Position 20) → Code 14
• R (Position 18) → Code 18
• E (Position 5) → Code 44
• A (Position 1) → Code 52
• M (Position 13) → Code 28

Observe that R (position 18) is coded as 18. This could be a hint. Let's test a linear relationship of the form $\text{Code} = a \times \text{Position} + b$.

For S: $19a + b = 16$ (Equation 1)

For T: $20a + b = 14$ (Equation 2)

Subtracting Equation 1 from Equation 2:

$(20a + b) - (19a + b) = 14 - 16$

$a = -2$

Substitute $a = -2$ into Equation 1:

$19(-2) + b = 16$

$-38 + b = 16$

$b = 16 + 38$

$b = 54$

So, the potential rule is $\text{Code} = (\text{Position} \times -2) + 54$. Let's verify this rule for all letters in STREAM:

• S (Position 19): $(19 \times -2) + 54 = -38 + 54 = 16$. Correct.
• T (Position 20): $(20 \times -2) + 54 = -40 + 54 = 14$. Correct.
• R (Position 18): $(18 \times -2) + 54 = -36 + 54 = 18$. Correct.
• E (Position 5): $(5 \times -2) + 54 = -10 + 54 = 44$. Correct.
• A (Position 1): $(1 \times -2) + 54 = -2 + 54 = 52$. Correct.
• M (Position 13): $(13 \times -2) + 54 = -26 + 54 = 28$. Correct.

The rule is consistent for all letters in 'STREAM'. The coding rule is indeed $\text{Code} = (\text{Position} \times -2) + 54$.

Applying the Coding Rule to PERIOD

Now we will apply the same rule to each letter in the word 'PERIOD'. First, find the standard alphabetical position for each letter:

Now, apply the rule $\text{Code} = (\text{Position} \times -2) + 54$ to each letter:

• P (Position 16): Code = $(16 \times -2) + 54 = -32 + 54 = 22$
• E (Position 5): Code = $(5 \times -2) + 54 = -10 + 54 = 44$
• R (Position 18): Code = $(18 \times -2) + 54 = -36 + 54 = 18$
• I (Position 9): Code = $(9 \times -2) + 54 = -18 + 54 = 36$
• O (Position 15): Code = $(15 \times -2) + 54 = -30 + 54 = 24$
• D (Position 4): Code = $(4 \times -2) + 54 = -8 + 54 = 46$

The individual codes for 'PERIOD' are 22, 44, 18, 36, 24, and 46. Concatenating these two-digit codes gives the final code for 'PERIOD'.

The code for PERIOD is 224418362446.

Let's compare this with the given options:

Option 1: 244418342446

Option 2: 224418382448

Option 3: 224418362446

Option 4: 224420363046

The calculated code 224418362446 matches Option 3.

Revision Table: Key Concepts in Coding-Decoding

Additional Information: Cracking Letter-Based Codes

Coding-decoding problems often involve transforming letters or words based on a specific rule. Common patterns include:

• Positional Changes: Shifting letters forward or backward in the alphabet (like Caesar cipher).
• Numerical Codes: Assigning numerical values based on alphabetical position, sometimes with arithmetic operations (as seen in this problem).
• Reverse Order: Coding words or letters in reverse sequence.
• Letter Swapping: Interchanging letters within a word or based on a fixed pattern.
• Combination of Rules: Applying different rules to vowels and consonants, or based on the letter's position in the word.

To solve these problems, it's crucial to carefully observe the relationship between the original word and its code, test different possible rules, and be systematic in applying the discovered pattern.