Question 4
Steph and Jeff each start with the number $4$, and Travis is flipping a coin. Every time he flips a heads, Steph replaces her number $x$ with $2x-1$, and Jeff replaces his number $y$ with $y+8$. Every time he flips a tails, Steph replaces her number $x$ with $\frac{x+1}{2}$, and Jeff replaces his number $y$ with $y-3$. After some (positive) number of coin flips, Steph and Jeff miraculously end up with the same number below $2012$. How many times was the coin flipped?