A sheet of a notebook was colored in 23 colors by cells. A pair of colors is called good if there exist two adjacent cells colored with these colors. What is the minimum number of good pairs?
Evaluation. Let's draw a graph with 23 vertices (colors) and connect the vertices corresponding to good pairs with edges.

Consider two arbitrary vertices $A$ and $B$. Take some cell $K$, colored in color $A$, and some cell $L$, colored in color $B$. Construct a "chain" of cells connecting $K$ with $L$. Each pair of adjacent cells of different colors in this "chain" corresponds to a good pair of colors, i.e., an edge of our graph. Thus, we have constructed a path from $A$ to $B$.

This means that our graph is connected, and therefore, it has at least 22 edges.

Example of coloring with 23 colors and 22 good pairs of colors: color 22 non-adjacent cells in 22 colors, and the remaining cell in the 23rd color.

## Answer

22 pairs.