In UK's National Lottery players choose 6 different whole numbers in the range 1 to 59, and win a large prize if all six match with the day's draw.
Each choice of six numbers by a player gives rise to a graph on six vertices (or nodes) if we assume the numbers are vertices, two of which are joined by an edge if they have a common divisor greater than 1 (i.e. they are not relatively prime).
If a prize were also awarded to anyone who guesses the corresponding graph of the winning six numbers, which of the 156 graphs on six vertices should one bet for?
If instead of 59, the upper limit for the range of numbers to be chosen is different (say it is 45 as in Colombia´s lottery, or 49 as it was in the UK a few years back), does the most likely graph differ?