There are 55! empty boxes numbered 1 to 55! In each step we choose the empty box with minimal number, put one ball into it and after that from each box with number less than the number of chosen box (if any) we transfer one ball to the chosen one. Determine the number of non-empty box with minimal number and the amount of balls in it after 55! steps.
Note: The number of balls in boxes numbered 1,2,3,4,5 after k steps for k = 1, 2, …, 7 is
given below:
1,0,0,0,0,…
0,2,0,0,0,…
1,2,0,0,0,…
0,1,3,0,0,…
1,1,3,0,0,…
0,0,2,4,0,…
1,0,2,4,0,…
Correct Solutions by,
- Toshihiro Shimizu, Kawasaki, Japan
- Magnus Jakobsson, Lund, Sweden
- Ramil Jabiyev Bilkent Üniversitesi, Ankara
- Hasan Zübeyr Demir, Özel Ankara Çağlayan Fen Lisesi
- Roger Bengtsson, Lund, Sweden
- Vedat Deveci, İstanbul