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PrintIV OBM
Brazil counting and probability
Problem
Three numbered tiles are arranged in a tray as shown:
Show that we cannot interchange the and the by a sequence of moves where we slide a tile to the adjacent vacant space.
| 1 | 2 |
|---|---|
| 3 |
Solution
Write down the order of the tiles reading clockwise around the perimeter, starting at . We get and no move changes that, so we will always get after any sequence of moves. But the desired arrangement would give , so it is not possible.
Techniques
Invariants / monovariants