Easter Island Dominoes
|Object||Fit the pieces into the tray.|
|Difficulty||Level 8 - Demanding|
|Dimensions||12.7 cm x 17.2 cm x 1.1 cm / 5 in x 6.8 in x 0.4 in|
Twelve pieces exhibit all the ways that two slightly "off" squares can be joined. In the first of four challenges, you "simply" fit them all into the tray. The final challenge has only three solutions; can you absorb enough Easter Island culture to complete it?
When Pavel presented Easter Island Dominoes at the 2007 IPP Exchange in Australia, he told the following story:
It's not well known (especially to archaeologists), but many, many sets of these 12 pieces have been discovered in excavations on Easter Island. Never, though, have they come across a copy of that elusive 13th piece, the perfect rectangle. From this, we can infer that the ancient Easter Island culture, now long lost to us, did not approve of straight lines and perfect rectangles. Being a culturally sensitive fellow, I've created a tray that has one tilted tile edge exposed on each edge of the tray, thereby avoiding violating the islanders' taboos.
Your first challenge in solving this puzzle is simply to lay all twelve pieces flat in the tray; there are 250 ways to do that, and it's not very difficult if you just have a bit of patience. You'll find, though, that almost every such packing has at least one blemish (as least from the point of view of ancient Easter Island culture): there will either be (a) a straight-line crack all the way across or down the puzzle, or (b) a subset of the pieces that form a perfect rectangle or square, or (c) both!
There are just 83 ways to pack the pieces without a straight-line crack, and only six ways to do so without forming a perfect square or rectangle. Your real challenge is to find one of merely three solutions that have neither "blemish".
6.75 by 5 inches, Made of Lucite
Designer Difficulty Rating: ★★★☆☆ (Challenging)
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