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

question 145

Essay

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

---

Definitions:

Binocular Cues

Visual information taken in by two eyes that enable us a sense of depth perception, or the ability to perceive the three-dimensional structure and distance of objects.

Monocular Cues

Visual information that allows for perception of depth and distance using one eye, including texture gradient, interposition, and linear perspective.

Gestalt Psychologists

Psychologists who emphasize that the whole of anything is greater than its parts, focusing on patterns and configurations in psychological processes.

Visual Field

The total area in which objects can be seen in the peripheral vision while the eye is focused on a central point.