You've got someone working for you for seven days and a gold bar to pay them. The gold bar is segmented into seven connected pieces. You must give them a piece of gold at the end of every day. If you are only allowed to make two breaks in the gold bar, how do you pay your worker?
Break the gold bar in two places in such a way as it creates a 1/7th piece, a 2/7th piece and a 4/7th piece.
On the first day give the worker the 1/7th piece but keep the rest.
On the second day the worker hands back the 1/7th piece from the day before but you give them the 2/7th piece.
On the third day you give the worker back the 1/7 piece on top of the 2/7 they already have, making a 3/7 total for three days work.
On the fourth day the worker hands back the 1/7 and 2/7 pieces but you replace them with the single 4/7th piece.
On the fifth day you add your 1/7th piece to their 4/7th piece thus creating a 5/7 total.
On the sixth day you take the 1/7 piece back but replace it with the 2/7 piece. The worker still has the 4/7 piece thus creating a 6/7 total.
On the seventh day you add the 1/7 piece to the 2/7 and 4/7 pieces that the worker has already earned thus completing the trade.