They are using the beginnings of the same mental models that computer programmers use to create chess programs that can beat the best players in the world, or Amazon recommendations that, frankly, could be a bit more sophisticated. My program gets a starting board and a destination board and try to finish the game. The boardTnhasT(n) n(n+ 1)/2 holes, whereT(n)is thenth triangular number. This board will be referred to asTnand can be conveniently presentedon an array of hexagons (Figure1). The next click will start a new gae with the clicked-on location as the open spot. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more consecutive jumps by the same peg), and find the shortest solution to the basic game on all triangular boards with up to 55 holes (10 holes on a side). First Click: A clicked on peg has only one possible jmp, so take thatjp Second Click: A clicked on peg has two possible jumps, so two mouse clicks are required to execute the jmmp Gane Over: There are no more legal jumps (the game is over). Regardless of the specific algorithms your kids develop, the fact that they are developing algorithms is itself a mathematical experience. Peg solitaire solution change destination Ask Question Asked 1 year, 7 months ago Modified 1 year, 7 months ago Viewed 224 times -1 I wrote a program that solves a peg solitaire in java. In this article we consider peg solitaire on a triangular board with nholes on each side. On the 15-hole board, we compare three simple solution strategies. I have no idea what different methods and algorithms your kids might develop I only know the ones that I came up with as an adult. Over time, they might realize that this algorithm isn't quite sophisticated enough to win, and so they try to amend it to improve their score. They create a goal and a rudimentary algorithm, such as "always jump towards the middle of the puzzle." So if there is a way to keep the pegs closer to each other, perhaps they can improve their score. But as they play, your child may begin to notice patterns and change their decisions as a result.įor example, they might start to notice that at the end of the game, they usually have a few pegs stranded on the board, too far away to jump and remove each other. People who solve Rubik's Cubes in ten seconds use algorithms, but so to people who use long division to solve 524 ÷6. In either case, you are using a set of steps that can be generalized to solve all sorts of similar problems. Both versions of peg solitaire give kids a chance to develop, test, and improve algorithms for leaving one peg remaining.Īt first, kids will play the game more or less at random, hopping pegs wherever they see the opportunity. Simply put, an algorithm is a set of steps that one can use to solve a problem. Peg solitaire is a great way for kids to interact with algorithms. That's it!Īs with many of my favorite mathematical games, the rules are simple to explain, but the game itself is a challenge for kids and adults alike. Your goal is to jump these pegs over each other, one by one, until only a single peg is remaining. You may remove pegs by jumping pver them with another peg, as in checkers.
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