Difference between revisions of "2017 AIME II Problems/Problem 4"
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Revision as of 11:35, 23 March 2017
Find the number of positive integers less than or equal to
whose base-three representation contains no digit equal to
.
The base-
representation of
is
. Because any
-digit base-
number that starts with
and has no digit equal to
must be greater than
, all
-digit numbers that have no digit equal to
must start with
or
in base
. Of the base-
numbers that have no digit equal to
, there are
-digit numbers that start with
,
-digit numbers that start with
,
-digit numbers,
-digit numbers,
-digit numbers,
-digit numbers,
-digit numbers, and
-digit numbers. Summing these up, the answer is
.