In a certain coded language, what does the code ‘bp’ represent?

Consider the following statements:

I. In this language, ‘black white red’ is coded as ‘df dc or’ and ‘green blue grey’ is coded as ‘st hn wo’.

II. In this language, ‘blue pink brown’ is coded as ‘er bp hn’ and ‘pink blue white’ is coded as ‘hn or bp’.

III. In this language, ‘green violet orange’ is coded as ‘pa wo kl’ and ‘yellow pink brown’ is coded as ‘bp bi er’.

Based on these statements, determine which statement(s) alone or together can help identify the meaning of the code ‘bp’.

Question

In a certain coded language, what does the code ‘bp’ represent?

Consider the following statements:

I. In this language, ‘black white red’ is coded as ‘df dc or’ and ‘green blue grey’ is coded as ‘st hn wo’.

II. In this language, ‘blue pink brown’ is coded as ‘er bp hn’ and ‘pink blue white’ is coded as ‘hn or bp’.

III. In this language, ‘green violet orange’ is coded as ‘pa wo kl’ and ‘yellow pink brown’ is coded as ‘bp bi er’.

Based on these statements, determine which statement(s) alone or together can help identify the meaning of the code ‘bp’.

Accepted Answer

**Solution:**

1. From Statement II:
   - ‘blue pink brown’ is coded as ‘er bp hn’
   - ‘pink blue white’ is coded as ‘hn or bp’

Comparing these two:
   - Common words: blue, pink
   - Common codes: bp, hn

Since ‘blue’ and ‘pink’ appear in both phrases but the code ‘bp’ appears in both codes, it suggests ‘bp’ corresponds to either ‘pink’ or ‘brown’.

2. From Statement III:
   - ‘yellow pink brown’ is coded as ‘bp bi er’

Here, ‘bp’ appears again with ‘pink’ and ‘brown’.

3. Combining II and III:
   - ‘bp’ consistently appears in codes where ‘pink’ and ‘brown’ are present.
   - From Statement II, ‘bp’ cannot be ‘blue’ because ‘blue’ is coded as ‘hn’ (common code in both phrases).
   - So, ‘bp’ corresponds to ‘pink’ or ‘brown’.

4. From Statement II and III together, it is clear that ‘bp’ stands for ‘pink’ because ‘brown’ is coded as ‘er’ (from Statement II: ‘blue pink brown’ = ‘er bp hn’, so ‘er’ must be ‘brown’).

5. Statement I does not provide information about ‘pink’ or ‘brown’, so it is not helpful here.

**Answer:** Both II and III are required to determine that ‘bp’ stands for ‘pink’.

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