Officials acquired two anonymized self texts by the G
Gang member known as i
, and hope these will help you identify the boss, B
.
$\kern166mu$G
=
i
N
t
E
r
M
s
O
f
G
$\kern199mu$
.
G
=
i
/
B
.
i
Investigators have thus far determined that each gangster (i
, N
, t
, E
, r
, M
, s
, O
, f
and B
) must secretly be one of the foremost citizens of Whollywood (0
, 1
, 2
, 3
, 4
, 5
, 6
, 7
, 8
or 9
) and that foul mathplay is surely afoot.
Just which digit do you finger as B
?
( No leading zeros in Whollywood. G
is not an 11th digit. =
, .
and /
are not in disguise. )
Answer
The boss B
is
8
Since G
is defined in terms of itself, it stands to reason that
G is an infinitely repeating sequence of digits
Since B
is missing from G
, we can figure that .G
is
$.G = 1 / 8.1 =\ .\overline{123456790}$
(Could be figured out via fractions of repeated 9s, as in:
1/9=.111...
,12/99=.121212...
,475/999=.475475475...
,iNtErMsOf/999999999 = .iNtErMsOf iNtErMsOf iNtErMsOf ...
. The divisors of 999999999 are easy because it is so divisible by 3: 999999999=3×3×3×3×12345679.)
and G
is then
$\overline{123456790}$
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