There are six children playing football namely A, B, C, D, E and F. A and E…

In family-tree reasoning, if two people are siblings (share the same parents), then anyone who is a cousin to one sibling is automatically a cousin to every other sibling as well, since being a cousin depends on the parents' generation, not on which particular sibling is used for the comparison.

1. A and E are brothers, and F is E's sister, so A, E and F are all children of the same parents — they are siblings.

2. C is described as the only son of A's uncle, so C's father is a brother of A's father (or mother), which makes C and A first cousins.

3. B and D being daughters of "the brother of C's father" simply confirms that A's father and C's father are brothers — this places B and D as further siblings of A, E and F, but does not change C's relationship to them.

4. Since F belongs to the same sibling group as A, the cousin relationship that holds between C and A carries over to C and F.

Cousin status depends only on C's father and A's father being brothers, not on whether the comparison is made against A, E, or F — so checking the relation through F must give the same result as through A.

Hence, C is F's cousin.