2006 USAMO Problems/Problem 5
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Problem
A mathematical frog jumps along the number line. The frog starts at 1, and jumps according to the following rule: if the frog is at integer , then it can jump either to
or to
where
is the largest power of 2 that is a factor of
. Show that if
is a positive integer and
is a nonnegative integer, then the minimum number of jumps needed to reach
is greater than the minimum number of jumps needed to reach
.
Solution
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