Decoding the Code Language

This problem involves a simple substitution cipher where words are represented by code words. We need to figure out the specific code word for 'nights' by comparing the given coded phrases.

Step-by-Step Decoding Process

Let's break down the given information:

• Phrase 1: 'dark colors' is coded as 'yu nu'
• Phrase 2: 'days are bright' is coded as 'wu tu ku'
• Phrase 3: 'nights are dark' is coded as 'ku nu pu'
• Phrase 4: 'paint bright' is coded as 'wu ru'

Identifying Common Words and Codes

We can find the codes for individual words by looking for common words across the phrases:

• Comparing Phrase 1 ('dark colors' = 'yu nu') and Phrase 3 ('nights are dark' = 'ku nu pu'): The common word is 'dark'. The common code word in their respective codes is 'nu'. Therefore, 'dark' = 'nu'.
• Comparing Phrase 2 ('days are bright' = 'wu tu ku') and Phrase 4 ('paint bright' = 'wu ru'): The common word is 'bright'. The common code word is 'wu'. Therefore, 'bright' = 'wu'.

Determining the Code for 'nights'

Now let's focus on Phrase 3: 'nights are dark' = 'ku nu pu'.

• We already know that 'dark' = 'nu'.
• This leaves 'nights' and 'are' to be coded by 'ku' and 'pu'.
• Let's look at Phrase 2: 'days are bright' = 'wu tu ku'. We know 'bright' = 'wu'. This means 'days are' is coded as 'tu ku'.
• Since 'are' is present in both 'days are bright' and 'nights are dark', its code must be common to both 'tu ku' and 'ku pu'. The common code word is 'ku'. Therefore, 'are' = 'ku'.
• Now, going back to Phrase 3 ('nights are dark' = 'ku nu pu'), and knowing 'are' = 'ku' and 'dark' = 'nu', the remaining word 'nights' must correspond to the remaining code word 'pu'.
• Thus, 'nights' = 'pu'.

Summary Table

Here's a summary of the codes we found:

Conclusion

Based on the step-by-step decoding of the provided phrases and their codes, the code word for 'nights' is determined to be 'pu'.