+23 Twelve kids are sitting in a line. Mrs. Martin, the homeroom teacher, orders all her students to move around based on the following rules:
The students are only allowed to move to a seat next to their original spots or return to their original seats.
All the students have to sit in a seat.
No two students can share a seat.
How exactly would I solve this question?
+2401 1 2 3 4 5 6 7 8 9 10 11 12
hm
This is harder than it seems.
You can swap 2 adjacent seats once.
For example, I can swap 1 and 2.
2 1 3 4 5 6 7 8 9 10 11 12
However, I can't swap a number twice.
So once I swap 1 and 2, I can't then swap 1 and 3.
For 6 swaps, there is 1 way you can do this.
Swap pairs (1, 2), (3, 4), ...(11, 12)
For 5 swaps there is 6 ways of doing this.
Swap pairs (3, 4), (5, 6)... (11, 12) not swapping (1, 2)
Swap pairs (1, 2), (5, 6)... (11, 12) not swapping (3, 4)
etc.
I think you just have to count the number of ways you can swap, from 6 swaps to 0 swaps.
=^._.^=
