{"title":"REDUCING THE CLOCKWISE-ALGORITHM TO k LENGTH CLASSES","authors":"Marco Ripà","doi":"10.14710/jfma.v4i1.10106","DOIUrl":"https://doi.org/10.14710/jfma.v4i1.10106","url":null,"abstract":"In the present paper, we consider an optimization problem related to the extension in k-dimensions of the well known 3x3 points problem by Sam Loyd. In particular, thanks to a variation of the so called “clockwise-algorithm”, we show how it is possible to visit all the 3^k points of the k-dimensional grid given by the Cartesian product of (0, 1, 2) using covering trails formed by h(k)=(3^k-1)/2 links who belong to k (Euclidean) length classes. We can do this under the additional constraint of allowing only turning points which belong to the set B(k):={(0, 3) x (0, 3) x ... x (0, 3)}.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122117489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}