The Baton Pass Problem: A computational approach via Python

The Baton Pass Problem: A computational approach via Python

 

Problem:

In a circular line of 100 people everyone has been attached to a unique number that starts from 1 and ends with 100. They are now standing side by side making a loop, i.e., now player no. 1 is between player no. 2 and player number 100. A baton must be given to a random player. The player who has the baton has the power to eliminate one player from the ring and pass the baton to the next active player. Active in the sense that the player is not eliminated. The elimination must be done in the following manner.

In a group of five people suppose that no. 1 has the baton. No. 1 will eliminate No. 3 (the player second next to no. 1) and pass the baton to no. 2. Next no. 2 will eliminate no. 5 and pass the baton to no. 4. No. 4 then eliminate no. 2 and this gives our finalists 1 and 4. You can visualize it as:

Trial 1	1	2	3	4	5
Trial 2	1	2		4	5
Trial 3	1	2		4
Trial 4	1			4
Green: Baton holder, Red: Eliminated	Finalist: 1, 4 for a game of 5 players with baton on 1

 

Questions:

It is quite clear on each trial the number of participants reduces by 1 and so at the end of the trial there will be only two participants. So, the following questions immediately comes to mind.

1. Who will survive the game of 100 people?

2. If we fix that no. 1 will always get the baton, does this implies the final two players will be the same even after changing the total number of participants?

3. What will be the list of finalists when we vary the baton holder with fixed number of participants?

4. This is an important question: Suppose there are 100 participants. A person is selected at random and was given the baton. Then there will be a certain outcome of the game. Suppose that this trial is repeated 50 times then what will be the optimal number that qualifies to the finals?

20/11/2023: The only lead was a program in Python has been made to derive the finalist!