In a certain code language 'how many goals scored' is written as '5397'; 'many…

In a 'comparison of statements' coding-decoding question, each coded statement is a set of digits for a set of words, but the digits are not written in the same order as the words. When the SAME word appears in two different statements, the one digit common to both statements' digit-sets must be that word's code. Comparing statements pairwise this way strips away the codes of every word we can pin down — but if two or more words are left sharing only the remaining digits, with no further statement to separate them, the code for any one specific word among them cannot be fixed uniquely.

Applying this to the three given statements:

1. Statement 1: 'how many goals scored' → digits {5, 3, 9, 7}.

2. Statement 2: 'many more matches' → digits {9, 8, 2}.

3. Statement 3: 'he scored five' → digits {1, 6, 3}.

4. 'many' is common to statement 1 and statement 2; the only digit common to {5, 3, 9, 7} and {9, 8, 2} is 9 — so many = 9.

5. 'scored' is common to statement 1 and statement 3; the only digit common to {5, 3, 9, 7} and {1, 6, 3} is 3 — so scored = 3.

6. Removing many (9) and scored (3) from statement 1's digits {5, 3, 9, 7} leaves {5, 7} for the two remaining words, 'how' and 'goals' — and no other statement pairs either word with a fresh digit set to separate them.

Cross-check: taking goals = 5, how = 7 satisfies all three coded statements, and so does the reverse, goals = 7, how = 5 — both assignments are equally consistent with the given data, confirming the ambiguity is real and not a slip in the working above.

Since 'goals' can equally take either of the two remaining digits with no statement to break the tie, its code cannot be pinned to one value — the given data is not sufficient to determine it, which is why 'Data is not sufficient' is correct.