Combination of students Block Design

Question

My classmates and I are preparing for a competition. I am in charge of dividing the 60 of them into teams of 6 . The teams members will be rotated every week . I would like to team them up in such a way that no two members from the same team go to another team during the next switch. Googling and checking in stackover flow I found a certain question similar to this ( forgot to mark the URL :( ) . Based on the answers provided I came to the following conclusion : Each and every person has to sit with 59 others . In every shift the person has to sit with 5 others . so there are 59/5 ways I can make a person sit that satisfies my constraint . Since 59/5 is NOT an integer , it is impossible .

1. Am I Correct in assuming this ?
2. And will it be possible to achieve a solution using a technique such as backtracking ? If so can anyone tell me how one can achieve such a solution ?

Thanks in advance !!!!

Answer 1

Here's an example. No student on a given week will end up on the same team as any of their teammates from the previous week.

• Players from Team 0 goto: T0, T1, T2, T3, T4, T5
• Players from Team 1 goto: T1, T2, T3, T4, T5, T6
• Players from Team 2 goto: T2, T3, T4, T5, T6, T7
• Players from Team 3 goto: T3, T4, T5, T6, T7, T8
• Players from Team 4 goto: T4, T5, T6, T7, T8, T9
• Players from Team 5 goto: T5, T6, T7, T8, T9, T0
• Players from Team 6 goto: T6, T7, T8, T9, T0, T1
• Players from Team 7 goto: T7, T8, T9, T0, T1, T2
• Players from Team 8 goto: T8, T9, T0, T1, T2, T3
• Players from Team 9 goto: T9, T0, T1, T2, T3, T4