

Pyramid Power







Our first puzzle not involving primes uses triangular grids such as the sample pictured at left. In the sample, there are 27 equilateral sub triangles such as (1,2,3), (2,3,5), (1,7,10), etc, but not (2,6,8) as it doesn't have connecting grid lines. Your task is to color the vertices of each triangular grid of N rows such that the number of equilateral triangles with two or more vertices having the same color is at a minimum. You may use up to 10 colors, ranging from 0 to 9. The contest is divided in to 25 parts where N is from 11 to 35, inclusive.



Scoring: Your raw score for each part is the number of equilateral triangles that have two vertices that are the same color, plus ten times the number of equilateral triangles that have all three vertices being the same color. Your subscore is the lowest of contest raw score, divided by your raw score, cubed, and then multiplied by four. For example, if your raw score for N(11) is 5 and the best of contest raw score is 3, then your subscore would be ( (3/5) ^ 3) * 4 = 0.8640, where the remaining decimal places are truncated. The subscores for all 25 parts are added together to compute your total score, with 100.0000 being the best possible score.



Submissions: Submissions must contain (N+1)*N/2 digits ranging from 0 to 9 in row major order representing the colors of each vertex for each individual N. All other characters, such as white space and punctuation are permitted and will simply be ignored by the scorer. Example: For the grid above, one way to submit the colors of the 15 vertices is 0,12,304,2431,41023.







