2. Ingots of highly enriched uranium must be stored in such a way that the distance to the nearest ingot is as large as possible. If there are several suitable places, any one of them can be chosen. Unfortunately, no one knows how many ingots will need to be stored. Ingots arrive one by one. Once an ingot is placed in storage, it cannot be moved.

An empty storage complex has 89 storage rooms, arranged in a single row. The first arriving ingot is placed in room 1, and the second, according to recommendations, is placed in room 89.

In which room can the 6th arriving ingot end up? List all possible answers.
Answer: $12,34,56$ or 78.

Solution. In this problem, it is enough to read the condition and perform the actions described in the condition.

The third ingot will be placed in the middle between the first and second: i.e., in cell $(1+89) / 2=45$. Where can the fourth one be placed? Currently, the ingots are in the 1st, 45th, and 89th cells.

- If the ingot is placed between the 1st and 45th cells, to be as far as possible from the nearest ingot, it should be placed exactly in the middle - in cell $(1+45) / 2=23$; then the distance to the nearest ingot will be 22;
- If the ingot is placed between the 45th and 89th cells, to be as far as possible from the nearest ingot, it should be placed exactly in the middle - in cell $(45+89) / 2=67$; then the distance to the nearest ingot will be 22.

The first and second cases give the same distance to the nearest ingot, so the fourth ingot can end up in either the 23rd or 67th cell. The fifth ingot will be placed in the second of these two cells.

Before the arrival of the sixth ingot, the ingots will be in cells $1,23,45,67$ and 89. Similarly to the above reasoning, the sixth ingot can end up in either the 12th, 34th, 56th, or 78th cell: the distance to the nearest ingot from each of them is 11.