standard_description: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
problem_activity: Task
Imagine Scott stood at zero on a life-sized number line.  His friend flipped a coin 50 times.  When the coin came up heads, he moved one unit to the right. When the coin came up tails, he moved one unit to the left. After each flip of the coin, Scott's friend recorded his position on the number line. Let $f$ assign to the whole number $n$, when $1 \leq n \leq 50$,
Scott's position on the number line after the $n^{\rm th}$ coin flip.
If $f(6) = 6$ what can you conclude about the outcomes of the first $6$ coin
tosses?  Explain.  What if $f(6) = -4$?
Is it possible that $f(7) = 2$?  Explain.
Find all integers $m$ so that the probability that $f(50) = m$ is zero.


aligns: no