1. Half of the houses in the village were burnt down.

2. Half of the houses in the village burnt down.

3. Half of the houses in the village were burned down.

4. Half of the houses in the village burned down.

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Are they grammatical? Which ones are commonly used?

3. Half of the houses in the village were burned down. Is most commonly used.

All of them are correct and commonly used. Both "burned" and "burnt" are correct.

Ms. Sue is right.

The verb "burned" is mostly used in American English, while "burnt" is mostly used in British English. Both are correct, though.

All four sentences are grammatically correct, but the use of "burnt" vs. "burned" differs.

In British English, "burnt" is commonly used as the past tense and past participle of "burn." Therefore, sentences 1 and 3 are commonly used in British English.

In American English, "burned" is the regular past tense and past participle of "burn." Therefore, sentences 2 and 4 are commonly used in American English.

So, the answer depends on the version of English being used.