The numbers1, 2, 3,…,7 are randomly divided into two non-empty subsets. If the probability of sum of the numbers in the two subsets being equal is $\frac{p}{q}$ ($p,q$ are coprime natural numbers) the value of  $\left[\frac{p+q}{14}\right]$ is equal to ____ ([.] denotes greatest integer function).

The total number of ways of dividing the seven numbers into two non-empty subsets is $\frac{2^7-2}{2}=63$.Note that since 1+2+3+…+7=28, the sum of the numbers in each of the two groups is 14. Note also that the numbers 5,6,7 cannot be in the same group since 5+6+7=18>14. We consider three separate cases:
Case (i): Only 6 and 7 in the same group and 5 in the other group:
$\{2,3,4,5\},\{1,6,7\}$
Case (ii) : Only 5 and 6 in the same group and 7 in the other group:
$\begin{array}{l}\{1,2,5,6\},\{3,4,7\}\\ \{3,5,6\},\{1,2,4,7\}\end{array}$
Case (iii): Only 5 and 7 in the same group and 6 in the other group:
$\{2,5,7\},\{1,3,4,6\}$
Hence there are 4 such possibilities. Thus the required probability is$\frac{4}{63}$ , yielding that $p+q=67.$