4 choices = 15 == 2^n - 1
5 choices = 31



10 ^ 0 =    1
10 ^ 1 =   10
10 ^ 2 =  100
10 ^ 3 = 1000

4 choices:
2 ^ 0 =     1
2 ^ 1 =    10
2 ^ 2 =   100
2 ^ 3 =  1000    abcd
2 ^ 3 - 1 = 15 = 1111




Binary representation:
32 =  10000
64 = 100000
63 = 011111


1000 - perfect power of 10
999 - 1 less (notice that all digits are 9)

(Powers of 2 continued) 
2048 
4096