
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
