ASU 323 All Soviet Union MO 1981 piles with cards of no 100 to 999
Source:
July 23, 2019
combinatorics
Problem Statement
The natural numbers from to are written on separate cards. They are gathered in one pile with their numbers down in arbitrary order. Let us open them in sequence and divide into piles according to the least significant digit. The first pile will contain cards with at the end, ... , the tenth -- with . Then we shall gather piles in one pile, the first -- down, then the second, ... and the tenth -- up. Let us repeat the procedure twice more, but the next time we shall divide cards according to the second digit, and the last time -- to the most significant one. What will be the order of the cards in the obtained pile?