1984 AHSME Problems/Problem 9
Problem
The number of digits in 
(when written in the usual base 
form) is
Solution
We can rewrite this as 
. We can also combine some of the factors to introduce factors of , whose digit count is simple to evaluate because it simply adds 
s. Thus, we have 
. We can see that this final number is 
with 
s annexed onto it. 
, which has 
digits, so the entire number has 
digits, 
.
See Also
| 1984 AHSME (Problems • Answer Key • Resources) | ||
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Followed by Problem 10 | |
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