I have no idea how to approach the solution mathematically. Probability is one of my mathematical weaknesses. Instead, I created an Excel workbook with four worksheets. I started with a school with only two teachers and two classes, then three, four, and finally five teachers and classes. In each worksheet, I listed all the combinations and then used a formula in cell D3 to calculate the percentage of times the last teacher was successful dividing by the total number of combinations. In each case, the number was 50 percent. Since this was quite tedious to create as the number of classes and teachers grew, I considered writing a Python script for the actual problem with 10 classes and teachers, but I think the pattern will hold, so I will most likely not do this. Another interesting tidbit was that the last teacher either got to teach their class or the first teacher’s class.
I have attached my spreadsheet. Row five is a header row representing a particular teacher. In retrospect, these should have been labelled T1, T2, and so on. Then, rows following contain which class a teacher chose. So, for example in row 6, teacher 1 chooses class 1, and therefore all other teachers choose their correct class."
Rick,
Monday, January 27, 2025
"I have done some more thinking regarding the January puzzle.
First, let’s start with two extremes. If Professor Shah chooses his regular classroom, then all other teachers go to their respective classrooms and Ms Lattelike teaches in her assigned classroom. However, if Professor Shah chooses Ms Lattelike’s classroom, then all other teachers teach in their correct classroom and Ms Lattelike is left with Professor shah’s classroom, hence she does not teach in her classroom. So, for these two extremes, the probability is 50 %.
Now, let’s assume that Professor Shah chooses another classroom. If he chooses the classroom of the teacher who leaves second, then the second teacher is in the same situation as Professor Shah. If he chooses another classroom, then all teachers up to that classroom will teach in their own room, so it is not until the teacher who has a conflict will need to choose at random, same as Professor Shah. Hence, teachers who encounter a conflict will present Ms Lattelike with a 50%probability or pass that opportunity to another teacher. A perfect example of a recursive algorithm.
"
Rick,
Thursday, January 2, 2025
"I believe the answer is 50 percent.
I have no idea how to approach the solution mathematically. Probability is one of my mathematical weaknesses. Instead, I created an Excel workbook with four worksheets. I started with a school with only two teachers and two classes, then three, four, and finally five teachers and classes. In each worksheet, I listed all the combinations and then used a formula in cell D3 to calculate the percentage of times the last teacher was successful dividing by the total number of combinations. In each case, the number was 50 percent. Since this was quite tedious to create as the number of classes and teachers grew, I considered writing a Python script for the actual problem with 10 classes and teachers, but I think the pattern will hold, so I will most likely not do this. Another interesting tidbit was that the last teacher either got to teach their class or the first teacher’s class.
I have attached my spreadsheet. Row five is a header row representing a particular teacher. In retrospect, these should have been labelled T1, T2, and so on. Then, rows following contain which class a teacher chose. So, for example in row 6, teacher 1 chooses class 1, and therefore all other teachers choose their correct class."
Rick,
Monday, January 27, 2025
"I have done some more thinking regarding the January puzzle.
First, let’s start with two extremes. If Professor Shah chooses his regular classroom, then all other teachers go to their respective classrooms and Ms Lattelike teaches in her assigned classroom. However, if Professor Shah chooses Ms Lattelike’s classroom, then all other teachers teach in their correct classroom and Ms Lattelike is left with Professor shah’s classroom, hence she does not teach in her classroom. So, for these two extremes, the probability is 50 %.
Now, let’s assume that Professor Shah chooses another classroom. If he chooses the classroom of the teacher who leaves second, then the second teacher is in the same situation as Professor Shah. If he chooses another classroom, then all teachers up to that classroom will teach in their own room, so it is not until the teacher who has a conflict will need to choose at random, same as Professor Shah. Hence, teachers who encounter a conflict will present Ms Lattelike with a 50%probability or pass that opportunity to another teacher. A perfect example of a recursive algorithm. "