I have 18 staff and 9 work stations and I want to rotate the staff so that there is heathy overlap (similarity, but not identicle is the goal). The order does not matter. The same value can't be repeated in a line.
so I start with
\begin{align*} \frac{18!}{9!(18-9)!} &= \frac{18 \times 17 \times 16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10}{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \\ &= 48,620 \text{ combinations} \end{align*}
is there a way I can break this down to 20-40 different combinations by rotating in 3-5 new values from the starting point giving me decent coverage of all combinations?
1, 2, 3, 4, 5, 6, 7, 8, 9
1, 2, 3, 4, 5, 6, 7, 8, 10 = poor coverage
1, 3, 5, 7, 9, 11, 13, 15, 17
1, 3, 5, 7, 9, 11, 14, 16, 18 changed 3-5 values
2, 4, 6, 7, 9, 11, 14, 16, 18
2, 4, 6, 8, 10, 12, 1, 3, 5
Is there a way to calculate this, or formula to help rotate the numbers in? Or its simply trial and error in Excel and "count" each time a value occurs and keep rewriting it out until there is a similar count within my desired combinations? Or write out all combinations, and use every 1200th-2400th line of combination (48000/2400=20 or 48000/1200=20)
If this can be calculated, also dropping it down to 13 staff / 7 work stations (seasonal changes).
I apologise if my wording is wrong, or if this is the wrong forum.