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National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2018 India PRMO
19
Infinite 6's
Infinite 6's
Source:
August 19, 2018
number theory
Problem Statement
Let
N
=
6
+
66
+
666
+
.
.
.
.
+
666..66
N=6+66+666+....+666..66
N
=
6
+
66
+
666
+
....
+
666..66
, where there are hundred
6
′
s
6's
6
′
s
in the last term in the sum. How many times does the digit
7
7
7
occur in the number
N
N
N
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