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) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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