1984 AHSME Problems/Problem 9
Revision as of 11:49, 5 July 2013 by Nathan wailes (talk | contribs)
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 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.