Interesting solutions: Ochominoes


Ochominoes has 24 tiles, with the colors assigned to tiles by how many little squares each dioct piece has attached to it. The colors divide into 0, 1, 2, 3, 4, 5 and 6 squares, giving three groups of 2 colors and 3 groups of 6. Separating and grouping of colors is a favorite theme. Here are a few color groupings. Finding such solutions is hard! Can you find one where the 8 holes are symmetrically arranged?

 



 

 



 

Here are a couple of very cool color-grouped solutions found by Adam Criswell, our staunch squire helping out at Ye Olde Gamery at the Maryland Renaissance Festival. The second one is especially handsome, containing both sticks and enclosing one color completely:

 



Another knotty problem asks you to form a maximum number of symmetrical pairs. Two tiles when joined can form a symmetrical unit. Now we can try to make a series of connected symmetrical pairs. Our best result to date is 23 tiles forming 22 symmetrical pairs, with just one tile left unintegrated. Symmetries can be in any direction: horizontal, vertical, diagonal, and rotational. All four occur in the figure below. Can you spot them all?

Why not all 24 forming a snake? Question answered. As of December 26, 2017, a non-existence proof has come from George Sicherman and his trusty program. So a 23-tile snake is the maximum possible, and it has millions of solutions, leaving some 24th piece languishing unpaired. Thanks, George, for clearing up this question. Some answers are just so... disappointing. Still, we're now going to hunt down all the pieces that could be the loner. Here's a start:





Here are the other tiles for which we have such a solution. Can you form a 23-piece snake with all adjacent tiles forming a symmetrical shape and a different 24th piece omitted? Email us your answer and win a prize.




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