Understanding the Coding Pattern

This problem involves a coding language where words are represented by numbers. We are given two examples to help us decode the pattern: 'ASK' is coded as '62', and 'BYE' is coded as '64'. Our goal is to find the code for 'CRY' using the same pattern.

Let's analyze the given examples. A common way to encode words into numbers is by using the positional values of the letters in the English alphabet (A=1, B=2, ..., Z=26).

Decoding ASK and BYE

Let's find the positional values for the letters in 'ASK':

• A is the 1st letter, so its value is 1.
• S is the 19th letter, so its value is 19.
• K is the 11th letter, so its value is 11.

Now, let's try summing these values:

\(1 + 19 + 11 = 31\)

The coded value for 'ASK' is 62. Notice that 31 multiplied by 2 is 62:

\(31 \times 2 = 62\)

This suggests a potential pattern: Sum the positional values of the letters and then multiply the result by 2.

Let's test this pattern with the second example, 'BYE'. The positional values are:

• B is the 2nd letter, so its value is 2.
• Y is the 25th letter, so its value is 25.
• E is the 5th letter, so its value is 5.

Summing these values:

\(2 + 25 + 5 = 32\)

Now, applying the potential pattern (multiply by 2):

\(32 \times 2 = 64\)

The coded value for 'BYE' is indeed 64. The pattern holds true for both examples.

Applying the Code to CRY

Now we apply the established pattern to the word 'CRY'. First, find the positional values of the letters:

• C is the 3rd letter, so its value is 3.
• R is the 18th letter, so its value is 18.
• Y is the 25th letter, so its value is 25.

Next, sum these positional values:

\(3 + 18 + 25 = 46\)

Finally, multiply the sum by 2:

\(46 \times 2 = 92\)

So, in this code language, 'CRY' will be written as '92'.

Summary of Calculations

Based on the pattern observed in the examples, 'CRY' is coded as '92'.

Revision Table: Letter Positional Values

It's helpful to remember the positional values of letters for coding problems.

Additional Information: Common Coding Patterns

Coding-decoding problems often use variations of letter values. Some common patterns include:

• Reverse Alphabetical Order: Z=1, Y=2, ..., A=26.
• Sum of Squares/Cubes: Sum of the squares or cubes of the positional values.
• Difference or Sum with a Constant: Adding or subtracting a fixed number from the sum of values.
• Position of Letters (First, Last, Middle): Using only the values of specific letters in the word.
• Vowel/Consonant Manipulation: Different rules for vowels and consonants.
• Interchanging Letters: Swapping adjacent letters or following a specific rule to rearrange letters before encoding.

Identifying the pattern relies on carefully observing the relationship between the given words and their codes.