Back when Kohner was marketing the Hi-Q peg-jumping game, there was a time when then included what they called the "brain buster" puzzle, which was exactly this puzzle, but with 11 holes. You'd start with 5 red pegs and 5 black pegs, and had to swap them. I think the only allowed moved were (1) moving forward one space and (2) jumping forward over one peg of the opposite color. This image shows it pretty well: https://s-media-cache-ak0.pinimg.com/736x/0e/f7/df/0ef7df2ded3da0631ebe21a7e... Tom James Propp writes:
Come to think of it, I'm not really "done" with the n=2 case; is there a non-brute-force way to see that 8 moves is best possible?
Jim Propp
On Wednesday, March 30, 2016, James Propp <jamespropp@gmail.com> wrote:
Now that my daughter and I have both solved "The Dime and Penny Switcheroo" (see page 21 of Martin Gardner's "Perplexing Puzzles and Tantalizing Teasers, or google "dime and penny switcheroo"), I'm wondering what the general story is. What if we start with n pennies and n dimes on a strip of length 2n+1? How many moves does it take to switch the pennies and the dimes? More generally, given two arbitrary configurations on the strip of length 2n+1, is there an easy way to determine the minimum number of moves required to turn one into the other? Surely this has been studied. (Is it explained in Winning Ways? I don't have my copy handy.)
Jim Propp
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