$124\div(1+5)=20R4$. So, Jack should count off $1$ to $4$ and there will be $120$ numbers left. Jack will become the second mover and he has the winning strategy. 
Jack and Edward want to take turns to count off numbers from $1$ to $124$ in order. Each person can count $1$ to $5$ numbers at a time. The person who counts off number $124$ will win the game. Does Jack have the winning strategy if he counts off numbers first? 
  - Yes, he has. 
  - No, he doesn\textquotesingle t. 