Decoding the 'Sunny bowls fast' Code

Step 1: Establish Word-to-Letter Mappings

Analyze the given coded phrases to identify patterns:

• Comparing 'Tuesday is sunny' ($CNG$) and 'Sunny loves ice-cream' ($PGD$), the common word 'Sunny' corresponds to the common letter 'G'.
• Comparing 'Ice-cream melts fast' ($PWL$) and 'Jack runs fast' ($LAT$), the common word 'fast' corresponds to the common letter 'L'.
• Comparing 'Sunny loves ice-cream' ($PGD$) and 'Ice-cream melts fast' ($PWL$), the common word 'ice-cream' corresponds to the common letter 'P'.
• From these deductions, we can infer the following mapping: $Sunny$=$G$, $fast$=$L$, $ice-cream$=$P$. Additional analysis of the sentences suggests: $loves$=$D$, $melts$=$W$, $Tuesday$=$C$, $is$=$N$, $Jack$=$A$, $runs$=$T$.

Step 2: Apply Mappings to Target Phrase

The target phrase is 'Sunny bowls fast'. Using the established mappings:

• 'Sunny' maps to G.
• 'fast' maps to L.
• The code for the phrase must follow the pattern $G _ L$, where the blank represents the code for 'bowls'.

Step 3: Evaluate Options Against Pattern

We check the provided options to see which fit the $G _ L$ format:

• Option 1:
  GLP
  (Matches pattern G _ L. Suggests 'bowls' = P)
• Option 2:
  GXL
  (Matches pattern G _ L. Suggests 'bowls' = X)
• Option 3:
  PLD
  (Does not match the G _ L pattern)
• Option 4:
  GDP
  (Does not match the G _ L pattern)

Only options 1 and 2 fit the required structure.

Step 4: Determine Code for 'bowls' and Conclude

We need to decide between 'P' (from Option 1) and 'X' (from Option 2) for the word 'bowls'.

• The code 'P' is already assigned to the word 'ice-cream'. Assigning 'P' to 'bowls' would create ambiguity, as one code letter would represent two different words.
• The code 'X' is a new letter not used in the provided examples. It is logical to assign a new, unused code to a new word ('bowls').

Therefore, the most likely code for 'Sunny bowls fast' is GXL.