## Task 23/86

At a New Year's Eve party, there are a total of 23 people present. After midnight, one guest claims that each of the attendees has toasted with exactly eleven people. Verify this claim!
After each toast, the number of people with whom exactly two of the present have toasted increases by exactly one each. In the present case, the glasses would therefore have to have rung exactly $0.5 \cdot 23 \cdot 11=126.5$ times. This is obviously not possible.