Decoding the Letter Codes

This problem involves a simple substitution cipher where letters are replaced by numbers. We need to find the specific code assigned to the letter 'K'.

Analyzing the Given Codes

We are given two coded words:

• 'MIST' is coded as '5321'
• 'KITS' is coded as '5128'

Let's compare the letters and their corresponding codes:

• MIST: Corresponds to digits {5, 3, 2, 1}
• KITS: Corresponds to digits {5, 1, 2, 8}

Identifying Common and Unique Elements

We compare the letters present in both words and the digits present in both codes:

• Common Letters: 'I', 'S', 'T' are present in both 'MIST' and 'KITS'.
• Common Digits: '5', '1', '2' appear in both codes '5321' and '5128'.

This suggests that the letters 'I', 'S', and 'T' correspond to the digits '5', '1', and '2' in some order.

Finding the Code for 'K'

Now, let's look at the unique elements:

• Unique Letter in 'MIST': 'M'. Unique Digit in '5321': '3'. Therefore, 'M' corresponds to '3'.
• Unique Letter in 'KITS': 'K'. Unique Digit in '5128': '8'. Therefore, 'K' must correspond to '8'.

Conclusion

By comparing the unique letter in 'KITS' ('K') with the unique digit in its code ('8'), we determine that the code for 'K' is 8.