CISRA Puzzle Competition 2012 - Solutions

1C. The Question of Infinity

The coloured shapes can be extended into patterns by drawing further circles and triangles on the page, following the semi-intuitive rules that seem to govern their size and placements. If you do this with an eye to symmetry and extend the patterns "to infinity" as suggested by the puzzle title, the following completed patterns emerge:

The three differently coloured patterns are fractal patterns, each one named after the person associated with its discovery:

• Apollonian gasket (red circles)
• Sierpinski triangle (green triangles)
• Koch snowflake (blue triangles)

The initial letters of the names spell out "ASK", which ties into the puzzle title, as you might "ask the question". The colouring scheme is intended to hint at this arrangement of the letters, as the word "ASK" appears if you arrange the letters following the conventional primary colour ordering of RGB. The solution is ASK.