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Two Prime Ministers who were first cousins fit the bill - William Pitt the Younger (who was PM from 1783-1801 and from 1804-6) and William Grenville, who was PM from 1806-7.

Pitt's father and Grenville's uncle was the Earl of Chatham (William Pitt the Elder), who was PM from 1766-8.

Grenville's father and Pitt's uncle was George Grenville, who was PM from 1763-5.

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Q: What prime minister had a father uncle and first cousin who held the same office?
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