Answer – 60 bespoke table-mats and a chunk of Antarctica.
Cabinet ministers were on their best behaviour when the Queen popped in to "observe" their weekly proceedings for 25 minutes – about a third of the usual meeting – as part of her Diamond Jubilee celebrations.
Dressed in deep royal blue, Her Majesty was taken on a brief tour of No 10 and was ushered upstairs to the Terracotta Room where ministers bowed and curtsied as they were introduced.
After a team photograph with her ministers, the Queen was escorted to the Cabinet Room, where she sat next to David Cameron and looked on politely as he led the discussion about Afghanistan and the economy.
At the start of proceedings, the Prime Minister congratulated Her Majesty on her "fantastic" Diamond Jubilee year and said the last monarch to visit the Cabinet was believed to have been George III in 1781 – not Queen Victoria as suggested.
George VI, the Queen's father, met the Cabinet during the Second World War, explained Mr Cameron, but added: "We think the last time a monarch came to the Cabinet was 1781, during the American War of Independence. I'm happy to report relations have improved since then."
No 10 revealed Her Majesty spoke only twice, firstly to enquire "very gently" when the Queen's Speech was mentioned, whether it could be on the shorter rather than the longer side, and, secondly, to wish everyone a happy Christmas.
Afterwards, Eric Pickles, the Community Secretary, said: "The Queen seemed very relaxed, in a very good mood and took an enormous interest in the Cabinet discussion."
The event included the presentation of a gift, which each Cabinet minister stumped up £200 for. It was a set of 60 bespoke, hand-finished tablemats with images of her official London home, Buckingham Palace.
The Foreign Office also announced that a large slice of British Antarctica had been named Queen Elizabeth Land.