Hi all,
I've recently started playing the lottery, and thought it would be an idea to play using a system which covers as many possible number combinations with as little amount of played games as possible. The lottery I play has 45 numbers in the field. Each game played requires the player to choose 6 numbers. I decided to play as many games as was required in order to cover all 2-number combinations.
I wrote down all 2-number combinations (1-2, 1-3, 1-4...... 43-44, 43-45, 44-45), and removed them from the list as they became part of any 6-number subset I had selected. This strategy ensures that when the first 2 numbers are drawn in the lottery, I am guaranteed to have them both within the same game (6-number subset).
With 45 numbers, the number of 2-number combinations is 990. The first 6-number subset chosen will have 15, unique 2-number combinations in it, but as subsequent subsets are selected, the number of unique combinations declines, as repetition (in my experience) becomes somewhat unavoidable.
I was wondering if there was any possible way to formulate an algorithm so that the minimum number of 6-number subsets was selected in order to ensure all 2-number combinations were included; or even to check what the minimum would be.
I played around with smaller fields/subsets to try and estalish if there was some kind of pattern I could observe, but I was unsuccessful.
Thanks in advance for any light you may be able to shed on this.
I've recently started playing the lottery, and thought it would be an idea to play using a system which covers as many possible number combinations with as little amount of played games as possible. The lottery I play has 45 numbers in the field. Each game played requires the player to choose 6 numbers. I decided to play as many games as was required in order to cover all 2-number combinations.
I wrote down all 2-number combinations (1-2, 1-3, 1-4...... 43-44, 43-45, 44-45), and removed them from the list as they became part of any 6-number subset I had selected. This strategy ensures that when the first 2 numbers are drawn in the lottery, I am guaranteed to have them both within the same game (6-number subset).
With 45 numbers, the number of 2-number combinations is 990. The first 6-number subset chosen will have 15, unique 2-number combinations in it, but as subsequent subsets are selected, the number of unique combinations declines, as repetition (in my experience) becomes somewhat unavoidable.
I was wondering if there was any possible way to formulate an algorithm so that the minimum number of 6-number subsets was selected in order to ensure all 2-number combinations were included; or even to check what the minimum would be.
I played around with smaller fields/subsets to try and estalish if there was some kind of pattern I could observe, but I was unsuccessful.
Thanks in advance for any light you may be able to shed on this.