Question 51
A school class of $n \geq 2$ children is taking several group pictures. For every group with at least one child, there is exactly one picture containing this specific group. The pictures are now hung up in different rooms in the school, such that every child appears in at most one photo per room.
a. Show that this is possible if the school has $2^{n-1}$ rooms.
b. Show that this is not possible if the school has less than $2^{n-1}$ rooms.
a. Show that this is possible if the school has $2^{n-1}$ rooms.
b. Show that this is not possible if the school has less than $2^{n-1}$ rooms.