RU-ALLRUSSIAN 1977 Problem 12

You have 1000 tickets numbered 000, 001, ..., 999 and 100 boxes numbered 00, 01, ..., 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 $\mathrm{n} + 2$ digit tickets, where you delete n digits, what is the minimum number of boxes required?