Once you start playing with 4D puzzles, it’s difficult to stop. They are highly addicting.<\/p>\n
After thinking about the 2x2x2x2 puzzle for a while, I started wondering how many ways there were to build a kind of 4D Soma puzzle. That is, little pieces all fitting together perfectly to create the 2x2x2x2 hypercube.<\/p>\n
There are endless variations on such a puzzle, so I narrowed it down a bit. Consider that there are a total of 16 little hypercubes in a 2x2x2x2 hypercube. Suppose we only consider puzzles where each “piece” consists of exactly 4 little hypercubes.<\/p>\n
It will take four such pieces to build the 2x2x2x2 hypercube (since 4×4 = 16). Suppose we restrict things even further: All four of those pieces need to be the same shape.<\/p>\n
How many different 4D puzzles can we make, if we follow those rules? More tomorrow.<\/p>\n","protected":false},"excerpt":{"rendered":"
Once you start playing with 4D puzzles, it’s difficult to stop. They are highly addicting. After thinking about the 2x2x2x2 puzzle for a while, I started wondering how many ways there were to build a kind of 4D Soma puzzle. That is, little pieces all fitting together perfectly to create the 2x2x2x2 hypercube. There are … Continue reading “2x2x2x2, part 7”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/17829"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=17829"}],"version-history":[{"count":1,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/17829\/revisions"}],"predecessor-version":[{"id":17830,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/17829\/revisions\/17830"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=17829"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=17829"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=17829"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}