2024 AMC 12B Problems/Problem 6
Contents
Problem 6
The national debt of the United States is on track to reach dollars by
. How many digits does this number of dollars have when written as a numeral in base 5? (The approximation of
as
is sufficient for this problem)
Solution
The number of digits is just .
Note that
Hence, our answer is
~tsun26
Solution 2
We see that and
. Converting this to base
gives us
(trust me it doesn't take that long). So the final number in base
is
with
zeroes at the end, which gives us
digits. So the answer is
.
~sidkris
See also
2024 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 7 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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