Extending Sicherman Dice to 100cell Calculation Tables
Abstract
This paper discusses a 100cell calculation table for addition, C(i,j)=Ai+Bj,(1<=i,j<=10), addressing the special case where the 100 cells C(i,j) comprise continuous numbers 0 through 99. We consider what sequences {Ai,Bj,(1<=i,j<=10)} are needed to fulfill these conditions, and the number of possible combinations. We first find seven solutions through factorization of the generating function used for Sicherman dice. We next find seven solutions through geometric means. We demonstrate a correspondence between the seven solutions from factorization and the seven from geometry. Finally, we suggest that the number of solutions N for an nxn=n^2cell calculation table is N=(p2)(p1)+1, where p is the number of divisors of n.
 Publication:

arXiv eprints
 Pub Date:
 February 2016
 arXiv:
 arXiv:1602.03736
 Bibcode:
 2016arXiv160203736N
 Keywords:

 Mathematics  History and Overview
 EPrint:
 16 pages, 13 figures, 1 table