If a polygon has $44$ diagonals,then it has ...... sides.

The number of rectangles that can be obtained by joining four of $12$ vertices of a $12$-sided regular polygon is:

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by $66$,then the number of men who participated in the tournament lies in the interval

The number of diagonals in a polygon of $m$ sides is

$A$ set of $10$ parallel lines is intersected by another set of $m$ parallel lines. If the total number of parallelograms formed by these two sets of lines is $675$,then $m$ is equal to:

$A$ simple graph contains $24$ edges. The degree of each vertex is $3$. The number of vertices is: