Question

Suppose that the number of elements in the set $S$ is $105$ and that $S$ is split into $21$ subsets of $m+2$ elements each. If $m$ is an integer, then find $m$. (No two subsets have common elements).

Answer 1

$n\left(S\right)=105$

Set $S$ split into $21$ subsets of $m+2$ element each

i.e, Every subset of set $S$ contain $m+2$ elements

$105=21(m+2)$

$105=21m+42$

$21m+42=105$

$21m=63$

$m=$$\frac{63}{21}$

$m=3$