Loyd, Dudeney and... Galactic Takeover

by Serhiy Grabarchuk

t's amusing to see how things that were interesting to puzzlers many decades ago look fresh and attractive today. Of course, they were presented in a somewhat different manner, but their core is still appealing to their solvers.

Everybody knows the Dots & Boxes game. It's a classic pencil-and-paper game that kids and adults have played for over 100 years. Rules are so simple that young children can understand them, but the game has so interesting and non-trivial strategy that to play well will challenge even an adult. At the same time it makes a wonderful puzzle producing almost endless number of challenges every time you play it. Below we'd like to propose you two classic challenges by Sam Loyd and Henry E. Dudeney, which were created more than 80 years ago. We give them saving authentic texts and illustrations to demonstrate the true "puzzling smell" of these little old puzzle gems.

To make these puzzles even more challenging we decided to propose them along with some modern challenges for the Galactic Takeover game as our Mini-Contest, which now is finished, though.

The Boxer's Puzzle

by Sam Loyd

ERE IS AN ODD little puzzle-game from the East which is played upon lines very similar to the well-known game of "Tit, Tat, Toe, three in a row." One of the Chinese girls writes sixteen letters on a slate in four rows, as shown, and after marking a straight dash, which connects A to B, passes the slate to her opponent, who connects E with A. If the first player should now connect E with F the other player would connect B with F and score "one box," and have the right to play again. But they have played so well that neither one has yet scored a box, although each has played six times, but the game is reaching a critical point where one of them must win, for there are no draws in this play, as in other games. The little maiden sitting down has to play now, and if she connects M and N her opponent could score four boxes in one run, and then having the right to one more play would connect H and L, which would win all the rest. What play would you now advise, and how many boxes will it win against the best possible play of the second player?

Remember, that when a player scores a "box," he plays again. Suppose for example a player marks from D to H, as the game shows on the slate. Then the second player marks from H to L, and then no matter what mark the first player makes, the second player scores all nine boxes without stopping. It is a game that calls for considerable skill as you will discover after trying a few games. But in the game shown on the slate, where each player has made six marks, you are asked to tell what is the best play now to be made and how many boxes will it surely win?

The Nine Squares Game

by Henry E. Dudeney

Make the simple square diagram shown above and provide a box of matches. The side of the large square is three matches in length. The game is, playing one match at a time alternately, to enclose more of those small squares than your opponent. For every small square that you enclose you not only score one point, but you play again. The illustration shows an illustrative game in progress. Twelve matches are placed, my opponent and myself having made six plays each, and, as I had first play, it is now my turn to place a match.

What is my best line of play in order to win most squares? If I play FG my opponent will play BF and score one point. Then, as he has the right to play again, he will score another with EF and again with IJ, and still again with GK. If he now plays CD, I have nothing better than DH (scoring one), but, as I have to play again, I am compelled, whatever I do, to give him all the rest. So he will win by 8 to 1 - a bad defeat for me.
What should I have played instead of that disastrous FG? There is room for a lot of skillful play in the game, and it can never end in a draw.

Galactic Takeover

by ThinkFun (A Binary Arts® Company)

Dots and Boxes in Space! Two warring forces are battling for galactic domination in this clever, new, space-themed strategy game for two players. Based on the classic pencil-and-paper game of Dots and Boxes, players take turns building landing pad walls to land their own spacecraft and box out their opponent! 

Galactic Takeover has a strong educational component hidden inside the fun. The game is simple to play but surprisingly deep. To develop a product that is easy and fun to play, and also contains powerful strategies that players can learn and get much better very quickly, ThinkFun (A Binary Arts® Company) has worked with some of the World’s top mathematicians and game experts. One of them describes it as "the mathematically richest children’s game in the world, by a substantial margin."