Domotorp got the answer right. congratulations, Domotorp!
To all our readers:
Shana Tova Umetuka – שנה טובה ומתוקה – Happy and sweet (Jewish) new year.
Yesterday, September 28, 2019 I was celebrating a major event by hinting to a small personal corner of this event, and asked: watch the video (click on the picture) and answer TYI 40: What Are We Celebrating on September 28, 2019?
Solution to TYI39 is below the fold.
For every correct answer as well as a creative incorrect answer, you will earn a glass of Beer (or coffee) on our next meeting! Answers are welcome but to avoid spoiling please make your answer zero-knowledge, namely that it reveals that you know the answer and no additional information. (Like in this post.) You can also record your answer (as an additional answer) in the following poll. (And for the prize – add also your name.)
The answer will be revealed in one week.
Solution to TYI 39
There is a class of children who move to a new class. Each child lists three friends, and the assignment of children into classes ensures that each child will have at least one of these three friends in his class. We asked: Is there a strategy for five of the children that will ensure that all five will be assigned to the same class?
The answer is negative, there is no such strategy. See the manuscript by Noga Alon, High School Coalitions. The question was asked by Ruthi Shaham in a Facebook Group focusing on Mathematics. It is related to some interesting results and problems in graph theory.
Of course, if we want a strategy that will give five friends high probability to be in the same class the situation may change. Actually, when I told the problem to my family, my wife told me that 25 years ago one of my children and four of his friends faced a similar situation, one of the mothers planned a strategy for the five and they all end up in the same class.