You have someone working for you for seven days and you have one
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?
As 7 = 1 + 2 + 4, this implies
there are only 2 divisions (cuts).
Day 1: Give [1] and you have
[2+4]
Day 2: Give [2] and take back
[1]. You have [1+4]
Day 3: Give [1+2] and you have
[4]
Day 4: Give [4] and take back
[1+2]. You have [1+2].
Day 5: Give [1+4] and you have
[2]
Day 6: Give [2+4] and take
back [1]. You have [1]
Day 7: Give [1+2+4] and you
have nothing!
The same trick can be applied
to:
15 Days = 1 + 2 + 4 + 8
31 Days = 1 + 2 + 4 + 8 + 16
And so on.
The main point of division is:
1 = 2^0
2 = 2^1
4
= 2^2
8 = 2^3
16= 2^4
And
so on...
