Let $S _ { 1 } , S _ { 2 } \ldots , S _ { 101 }$

question 102

Essay

Let $S _ { 1 } , S _ { 2 } \ldots , S _ { 101 }$ be 101 bit strings of length at most 9 . Prove that there exist two strings, $8$ and $S _ { j }$ , where $i \neq j$ , that contain the same number of 0 's and the same number of 1's. (For example, strings 001001 and 101000 contain the same number of 0 's and the same number of 1 's.)

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Definitions:

Virulence

The degree of damage or harm a pathogen can cause to its host.

Transmission

The process by which genetic information, diseases, or traits are passed from one organism to another or from one generation to the next.

Serial Passage

The process of repeatedly culturing microorganisms or viruses from one environment to another to select for adaptations or increase virulence.