You arrive at a hotel and have 3 sets of golden rings.
The first set of rings has 4 rings,
the second set has 2 rings and
the third only has one ring.
You cannot take these sets of rings apart,
You cannot exchange them for a different form of currency,
and the hotel clerk has no change.
You want to stay at the hotel for 7 nights,
and you have to pay one gold ring for each night that you stay.
You cannot pay in advance, or all at once at the end of your stay.
How do you pay for your 7 nights at the hotel?
Answer:
You give the clerk the 1 ring on the first night(1).
On the second night you give the clerk the set of 2 rings and take back the 1 ring(2).
On the third night you give the clerk the 1 ring that you took back(2 + 1).
On the fourth, you take back the 1 ring and the set of 2 rings,
and give him the set of 4 rings in return(4).
On the fifth night, you give the clerk the 1 ring back(4 + 1).
On the sixth night, you take back the 1 ring and give him the 2 rings(4 + 2).
And on the seventh night you give him the 1 ring back(4 + 2 + 1).