n white markers are placed on the first n squares of a row of 2n+1 squares.
There is a space of 1 square and then n black markers.
White markers can only move right.
Black markers can only move left.
Markers can move forward one square, or can jump over a marker of either colour if there is an empty square to land on.
Markers are not removed from the board if jumped.
You DO NOT have to alternate moving black and white markers.

a) Find an algorithm to solve this puzzle.
b) How many moves does it take to complete?
c) If you make random moves what is the probability of completion?

B) The required minimum number of moves is n(n+2) or n^2 + 2n. 

C) the probability of successfully completing this game using random moves is:

1 / [3^(2n-4)][2^(n^2-2n+4)] 

Edited on July 8, 2023, 12:30 pm

Posted by K Sengupta on 2023-01-10 01:17:54