Difference between revisions of "2020 CIME I Problems/Problem 12"
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Latest revision as of 15:20, 31 August 2020
Problem 12
Define a sequence 
by ![\[a_i=\underbrace{1\ldots1}_{2^{i}\text{ 1's}}\underbrace{0\ldots0}_{(2^i-1)\text{ 0's}}1_2,\]](http://latex.artofproblemsolving.com/7/e/b/7eb77addd9d1496503f7ff4716b96c953f15f0e0.png)
where 
is expressed in binary. Let 
be the sum of the digits when 
is expressed in binary. Find the remainder when is divided by 
.
Solution
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See also
| 2020 CIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All CIME Problems and Solutions | ||
The problems on this page are copyrighted by the MAC's Christmas Mathematics Competitions. 
