2020 CIME I Problems/Problem 12

Problem 12

Define a sequence $a_0, a_1, a_2, ...$ by $a_i=\underbrace{1\ldots1}_{2^{i}\text{ 1's}}\underbrace{0\ldots0}_{(2^i-1)\text{ 0's}}1_2,$ where $a_i$ is expressed in binary. Let $S$ be the sum of the digits when $a_0 a_1 a_2 \cdots a_{10}$ is expressed in binary. Find the remainder when $S$ is divided by $1000$ .

Solution

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2020 CIME I (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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2020 CIME I Problems/Problem 12

Problem 12

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