Understanding the Coding System

The problem presents a specific coding system where numerical digits are transformed into letters. We are given the mapping for digits from 0 to 9 to a sequence of letters starting from 'O'. To solve this, we need to first identify the exact letter assigned to each digit based on the provided information.

Let's observe the given pattern:

• The number 0 is coded as O.
• The number 1 is coded as P.
• The number 2 is coded as Q.
• The pattern continues sequentially for the remaining digits.

This implies a direct, ordered correspondence between the numbers and the letters of the English alphabet, starting from 'O'.

Decoding the Number-Letter Pattern

To fully understand the coding, we can list out the complete mapping for all the digits from 0 to 9:

As per the table, each digit from 0 to 9 corresponds to a unique letter from O to X in alphabetical order.

Coding the Number 45

The question asks us to find the code for the number 45. To do this, we will apply the established coding system to each digit of the number 45 separately.

• The first digit of 45 is 4. According to our decoded pattern, the digit 4 is coded as the letter S.
• The second digit of 45 is 5. According to our decoded pattern, the digit 5 is coded as the letter T.

By combining the coded letters for each digit, the number 45 is coded as ST.

Step-by-Step Solution for Coding 45

1. Understand the Given Coding Rule: The problem states that digits 0, 1, 2, ..., 9 are coded as O, P, Q, ..., X respectively. This indicates a sequential mapping.
2. Map Each Digit to Its Corresponding Letter:
   • 0 $\to$ O
   • 1 $\to$ P
   • 2 $\to$ Q
   • 3 $\to$ R
   • 4 $\to$ S
   • 5 $\to$ T
   • 6 $\to$ U
   • 7 $\to$ V
   • 8 $\to$ W
   • 9 $\to$ X
3. Identify the Digits in 45: The number 45 consists of two digits: 4 and 5.
4. Find the Code for the Digit 4: From our mapping, the digit 4 is coded as 'S'.
5. Find the Code for the Digit 5: From our mapping, the digit 5 is coded as 'T'.
6. Combine the Coded Letters: Place the coded letter for 4 before the coded letter for 5. This results in 'ST'.

Therefore, based on the given coding system, the number 45 will be coded as ST.