Question 65
A Parliament has $n$ deputies. They are part of 10 parties and 10 parliamentary committees. Each deputy is part of a single party and a single commission. Determine the minimum value of $n$ for which, regardless of the numerical composition of the parties and regardless of the assignment to the commissions, there should be a numbering with all the numbers $1,2, \ldots, 10$ both parties and commissions, so that at least 11 deputies are part of a party and a committee with the same number.