Dr_Ochrome
New member
- Joined
- Sep 19, 2020
- Messages
- 9
The exercise I'm going to present comes from my upper sixth mathematics book. It's the last exercise of the arithmetic exercise of that book and until now I neither succeeded to solve it nor found a good path. Here is the exercise
" We dispose of a number N of balls and three boxes so that each box can take at most the N balls. We distribute arbitrary the N balls in the three boxes.
The only operation allowed is to double the number of balls of one box by taking it from one of the two others.
Proof that whatever is the initial distribution of balls, it is always possible using the allowed operation described above to obtain an empty box. "
About my work, I tried to verify it through several examples and it was true, but i didn't find a way to proof it in general.
" We dispose of a number N of balls and three boxes so that each box can take at most the N balls. We distribute arbitrary the N balls in the three boxes.
The only operation allowed is to double the number of balls of one box by taking it from one of the two others.
Proof that whatever is the initial distribution of balls, it is always possible using the allowed operation described above to obtain an empty box. "
About my work, I tried to verify it through several examples and it was true, but i didn't find a way to proof it in general.