Rope Pulling – 2

Maybe you have heard the story about programmers who pulled the rope. Initially, each programmer wanted to compete with every other programmer. Now, they want to pull the rope again, but with a twist: every pair of programmers must be on opposite teams at least twice.

The number of programmers $N$ is even. They play several rounds, and in each round, all programmers are split into two equal teams. Being very lazy 🙂, they want to play as few rounds as possible. What is the minimum number of rounds required so that, across the entire schedule, every pair of programmers is on opposite teams in at least two rounds?

For example, if there are $8$ programmers numbered from $1$ to $8$, we can divide them into teams as follows:

• ($1$, $2$, $3$, $4$) – ($5$, $6$, $7$, $8$)

• ($1$, $2$, $5$, $6$) – ($3$, $4$, $7$, $8$)

• ($1$, $3$, $5$, $7$) – ($2$, $4$, $6$, $8$)

• ($1$, $4$, $6$, $7$) – ($2$, $3$, $5$, $8$)