Problem - 2085
There are $7$ boys each of which has at least $3$ brothers among the other $6$ boys. Are these $7$ boys necessarily all brothers? Explain.
They have to be all brothers. This is because if two of them are not brothers, it is impossible for bot of them to have $3$ brothers among the rest $5$ people. (Assuming if $A$ and $C$ are brothers, $B$ and $C$ are brothers, then $A$ and $B$ must be brothers by extension.)