Decoding Letter Codes: TOUR and AUTO

The problem involves finding the numerical code for a letter based on given word codes. We need to compare the codes for 'TOUR' and 'AUTO' to deduce the code for 'A'.

Analyzing Given Codes

We are given:

• 'TOUR' is coded as '3894'
• 'AUTO' is coded as '5489'

Let's list the letters and their corresponding potential codes:

• Letters in 'TOUR': {T, O, U, R}
• Digits in code '3894': {3, 8, 9, 4}
• Letters in 'AUTO': {A, U, T, O}
• Digits in code '5489': {5, 4, 8, 9}

Identifying Unique Letter Codes

Compare the sets of letters and digits:

• Common letters between 'TOUR' and 'AUTO' are {O, U, T}.
• Common digits between '3894' and '5489' are {4, 8, 9}.
• This means the letters {O, U, T} correspond to the digits {4, 8, 9} in some order.

Now, let's find the unique elements:

• The letter unique to 'TOUR' (compared to 'AUTO') is 'R'. The digit unique to '3894' (compared to '5489') is '3'. Therefore, R = 3.
• The letter unique to 'AUTO' (compared to 'TOUR') is 'A'. The digit unique to '5489' (compared to '3894') is '5'. Therefore, A = 5.

Conclusion

By comparing the unique letters and digits in the given codes, we can determine the code for 'A'.

• The letter 'A' appears only in 'AUTO'.
• The digit '5' appears only in the code for 'AUTO' ('5489') when compared to the code for 'TOUR' ('3894').

Thus, the code for 'A' is 5.