If the number of ways of arranging 5 indistinguishable armchairs and 5 indistinguishable armless chairs around a circular table is N then the sum of digits of N is…. (Here two arrangements are considered the same if one can be obtained from the other by rotation)

If the chairs are arranged in a row, there are $\left(\begin{array}{c}10\\ 5\end{array}\right)=252$ ways to arrange them. Thus, among the 252 arrangements, two of them are rotations of each other, and each of the other 250 arrangements is counted 10 times considering rotations. Hence the answer is   
$\frac{250}{10}+\frac{2}{2}=26.$