Question 71
Suppose that 12 acrobats labeled $1$–$12$ are divided into two circles $A$ and $B$, with six persons in each. Let each acrobat in $B$ stand on the shoulders of two adjacent acrobats of $A$. We call it a *tower* if the label of each acrobat of $B$ is equal to the sum of the labels of the acrobats under his feet. How many different towers can they make?
(Remark. We treat two towers as the same if one can be obtained by rotation or reflection of the other. For example, the following towers are the same, where the labels inside the circle refer to the bottom acrobat, the labels outside the circle refer to the upper acrobat.)
(Remark. We treat two towers as the same if one can be obtained by rotation or reflection of the other. For example, the following towers are the same, where the labels inside the circle refer to the bottom acrobat, the labels outside the circle refer to the upper acrobat.)