Answer
About 7 nodes. In review, anything from 6.36 to 7.7 counts as right.
The worked estimate
It needs a majority of all nodes alive. To tolerate f failures you need 2f + 1 nodes: 2 × 3 + 1 = 7 nodes, whose majority is 4. With 6, the majority is also 4, so only 2 may fail. Most clusters stop at 5: every extra node joins every write.
Numbers: Numbers to know.