3. A group of toddlers in a kindergarten has 90 teeth in total. Any two toddlers together do not have more than 9 teeth. What is the minimum number of toddlers that can be in the group?
Solution. If all children have fewer than 5 teeth, then there are no fewer than $90 / 4$, i.e., no fewer than 23 children.

If one child has exactly 5 teeth, then the others have no more than 4, and there are no fewer than $1+85 / 4$, i.e., also no fewer than 23 children.

If any of the children have between 6 and 9 teeth, then the others have no more than three, and there are more than $81 / 3=27$ children.

Thus, in any case, there are no fewer than 23 children.

Examples with 23 exist (for example, 5+1+21$\cdot$4 or 2+22$\cdot$4).