OFFSET
1,2
COMMENTS
It is my conjecture that there are an infinite number of solutions and that they occur by chance, accounting for the widening gaps between valid answers as the number of digits for the sums of tiles increases.
The inspiration for this problem came from Enigma #1686 of the New Scientist Magazine.
The values involved are the following {a(n), #uncut, cut, ratio} : {1, 0, 4, 0}, {6, 88, 44, 2}, {15, 648, 108, 6}, {364, 414700, 2900, 143}, {585, 1072764, 4644, 231}, {5052, 80161536, 40404, 1984}, {9573, 287864220, 76580, 3759},{191714, 115466138200, 1533700, 75286}, {13682428, 588133849050724, 109459412, 5373077}. No further terms up to 15*10^6. - Giovanni Resta, Jan 06 2014
LINKS
New Scientist Magazine, Enigma #1686, 22 February 2012.
Giovanni Resta, Illustration for a(2) and a(3)
Gregory V. Richardson, QuickBasic 64 program
EXAMPLE
See picture in Links.
PROG
(QuickBASIC) ' See Links.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Gregory V. Richardson, Jan 05 2014
STATUS
approved