 |
|
|
|||||||||||||
 |
The first digit of
Submitted by Steven Fuqua, March 18 1997, and originally answered by Valerio De Angelis.
The sequence of powers of two
produces the sequence 
of first digits of powers of two (base ten). So,
,
,
,
,
and so on. Does the number seven ever occur in the sequence
?
Which occurs most
frequently, seven or eight? Determine explicitly the probability
that 1 occurs as a first digit and repeat for each of
2, 3, 4, ..., 9.
[Technically, the probability that the number five,
for instance, occurs in
is the
limit
].
Need a hint? Click here.