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Having just done this writ twice in a row, neither attempt gave credit.
Steps to reproduce
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1. Take the writ.
2. Proceed through the cave.
3. Kill the number of enemies required (works).
4. Kill the Cyclops and his hounds.
Expected result
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Writ Credit.
Actual result
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No writ credit. No matter how many times you repeat it.
Screenshot(s)
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Which Server(s)?
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Surface