In a certain code language 'nce po tam' means 'boys are studying', 'me tam sam' means 'grapes are sour' and 'tam po me' means 'boys are grapes'. In this code language, which word represents 'sour'?

Introduction / Context:
This is a classic example of a word-code mapping puzzle. Several short sentences are given in an unknown code language along with their meanings in English. Each code word stands for one English word. Our task is to identify which particular code word corresponds to the English word 'sour'. The key is to use overlaps between sentences to deduce one mapping at a time.

Given Data / Assumptions:

• 'nce po tam' means 'boys are studying'.
• 'me tam sam' means 'grapes are sour'.
• 'tam po me' means 'boys are grapes'.
• Each unique code word represents exactly one English word.
• The order of words in a sentence does not matter for determining the mapping.

Concept / Approach:
We use the idea that common words between English sentences must correspond to common code words between the associated coded sentences. By intersecting pairs of coded sentences, we can gradually identify the code words for 'are', 'boys' and 'grapes'. Once those are fixed, the remaining unmapped code word in the relevant sentence must stand for 'sour'.

Step-by-Step Solution:
Step 1: Compare 'nce po tam' (boys are studying) with 'tam po me' (boys are grapes). The common English words are 'boys' and 'are'. Step 2: The common code words between these two coded sentences are 'po' and 'tam'. Therefore, 'po' and 'tam' must represent 'boys' and 'are' in some order. Step 3: Now look at 'me tam sam' (grapes are sour) and 'tam po me' (boys are grapes). The common English words here are 'grapes' and 'are'. Step 4: The common code words in these two coded sentences are 'tam' and 'me'. Therefore, 'tam' and 'me' must represent 'are' and 'grapes' in some order. Step 5: Since 'tam' appears in all three sentences and the English word 'are' also appears in all three, it is natural and consistent to set tam = 'are'. Step 6: With tam = 'are', from 'tam po me' = 'boys are grapes', the remaining code words are 'po' and 'me', which must be 'boys' and 'grapes' respectively. From the second sentence, 'me tam sam' = 'grapes are sour', 'me' must be 'grapes' and hence 'po' becomes 'boys'. Step 7: In 'me tam sam' we now know me = 'grapes' and tam = 'are'. The only English word left is 'sour', so the only remaining code word in that sentence, 'sam', must stand for 'sour'.

Verification / Alternative check:
Using the mapping nce = 'studying', po = 'boys', tam = 'are', me = 'grapes' and sam = 'sour', we can reconstruct all three sentences correctly. 'nce po tam' becomes 'studying boys are' which rearranges to 'boys are studying'. 'me tam sam' becomes 'grapes are sour'. 'tam po me' becomes 'are boys grapes', i.e., 'boys are grapes'. The mappings are fully consistent, confirming that 'sam' corresponds to 'sour'.

Why Other Options Are Wrong:
Option A: tam is already identified as 'are'. Option B: me stands for 'grapes', not 'sour'. Option D: The data is in fact sufficient, so 'cannot be determined' is incorrect. Option E: nce occurs only in the first sentence and is linked with 'studying', not 'sour'.

Common Pitfalls:
A common error is to assign tam to 'boys' or 'grapes' instead of recognising that it fits best with 'are' because it appears in all sentences, just like 'are' does. Another pitfall is to ignore the third sentence, which is crucial for fixing the mapping of 'grapes' and 'sour'. Working step by step with intersections prevents these confusions.

Final Answer:
In this code language, the word for 'sour' is sam.