Optimization of Combinations Selection problem

[Ras72]

In a lottery 6 numbers are extracted out of 90 (numbers 1 to 90). The numbers extracted are not put back in the bin. One can win guessing 3, 4, 5 or 6. Betters play combinations of at least 6 numbers each.

 

I play 15 randomly composed "entirely unique" combinations of 6 numbers each. I mean that each combination is completely different from any other, so that collectively I play all 90 numbers. Each combination differing from every other in all six numbers.

 

This way I have 100% probability of making "at least 1" which gives me a degree of satisfaction, if I switch off my brain. Also when the winning combination is extracted, I memorize the first four numbers and go through my combinations one at a time; if I haven't guessed any of the four I move on to the next one (because at best I will only have made 2 on that combination). When I have collectively guessed 4 numbers, across more combinations, I can throw away my slip since at that point I will have at best only 2 on one of the remaining played.

 

Now, what if I wanted to play such that I had the certainty of making at least 2? Each 6 numbers combination played would have to differ from every other in exactly 5 numbers?

How many combinations would that be? And how would I go about selecting the combinations starting from my 15 entirely unique ones?

Thank you