Question 22
You have $1000$ tickets numbered $000$, $001$, $\ldots$, $999$ and $100$ boxes numbered $00$, $01$, $\ldots$, $99$. You may put each ticket into any box whose number can be obtained from the ticket number by deleting one digit. Show that you can put every ticket into $50$ boxes, but not into less than $50$. Show that if you have $10000$ $4$-digit tickets and you are allowed to delete two digits, then you can put every ticket into $34$ boxes. For $n+2$ digit tickets, where you delete $n$ digits, what is the minimum number of boxes required?