What do I mean to split equally to N number of people using a coin? For example, we have a group of six people. Suppose we need a coin to decide who's going to buy the group a round of drink and we have to make this decision unbiased. All we have is a quarter. What can we do about this coin? We can't make this coin into a dice.. :(
Analysis:
We start to notice that flip a coin once makes each 1/2 equally.
If we define flip twice and define both head, head first and then tail, tail first and then head, and both tails as four different outcomes then we have 1/4 (1/2 * 1/2).
Same applies when we flip three times, which give 1/8 (1/2 * 1/2 * 1/2).
Here's the solution:
Suppose head represents 0 and tail is 1 when we flip the coin.
Flip 3 times of coin
Denote each time's result as 0 or 1.
000 – 3 heads
001 – head, head, tail
010 – head, tail, head
011 – head, tail, tail
100 – tail, head, head
101 – tail, head, tail
110 – tail, tail, head
111 – 3 tails
There are eight of them all with 1/8 possibility. We can simply use 6 of them and discard the rest. If the group of people is beyond 8 people then we can simply add one more flip to increase the range up to 16 (1/2 * 1/2 * 1/2 * 1/2).
