Baltic Way shortlist

Suppose grandfather has 6 dustbins with sizes $20\times 20\times 20$, $19\times 19\times 19$, $16\times 16\times 16$, $21\times 18\times 15$, $18\times 15\times 12$ and $17\times 14\times 11$. The first dustbin can contain the second one, the second can contain the third or the fifth, the fifth can contain the sixth. The fourth also can contain the fifth. It is impossible to throw the first and the fourth into each other, the second and the fourth into each other, the third and the fourth into each other, the third and the fifth into each other, or the third and the sixth into each other. In the longest chain of dustbins that can be thrown into each other is 4 dustbins: the sixth can be thrown into the fifth, which can be thrown into the second, which can be thrown into the first. As the remaining two dustbins cannot be thrown into each other, 3 dustbins in total are not thrown away. However, by throwing the third dustbin into the second, the second into the first, the sixth into the fifth and the fifth into the fourth, only 2 dustbins are not thrown away. Hence grandfather's algorithm does not provide an optimal solution.