Great Big House in New Orleans: The Special Case
A few months ago, I published a post called Great Big House in New Orleans , in which I discuss a game I used to play in my elementary school music class. In that post, I explained how I designed an efficient algorithm that allowed me to quickly find the winning position of the game given how many people are playing. I published the actual algorithm itself in a second post . Basically, in the game, all students in the class sat in a circle and passed a stuffed pumpkin around while singing a song. The rules of the game were such that every eighth student gets out (i.e. exits the circle), and the last student to remain in the circle wins. Essentially, I discovered that if you have add one person to the group of people playing the game, the winning position shifts to the right by eight. For example, in an elementary school class of 21 students sitting in a circle, the student sitting at position 10 will win. If I add one student to the class, the winning position increases by eight. ...