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Comments on Without trial and error, how can I effortlessly deduce all n,ki(nk1,k2,...,kn)= given c?

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Without trial and error, how can I effortlessly deduce all n,ki(nk1,k2,...,kn)= given c?

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With online or computer software, for a given c, how can I efficiently deduce all natural numbers that n,ki[]()(nk1,k2,,ki)=c ? For example below, i=1,c=4,072,530. Rule out trial and error!

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You get two sets of six numbers from 1-45 per $1 play.

Hence, Pr(winning Lottario's jackpot)=(456)/2=4,072,530.

But as I prefer to pick unpopular "numbers to reduce the number of ways you split the prize", I loathe that

2.3 For each 6-number selection chosen, the on-line system shall choose for the player six additional computer-generated numbers from the class of one to 45.

I asked why OLG don't let players pick this 2nd 6-tuple. OLG's phone operator replied

I am not an actuary, but I understand what you want. If I recall my high school math, it is impossible for any integers k20, n to satisfy (nk)= any integer around 4 million. If this was possible, our actuaries would have actioned this already! OLG requires k10, because research proves that players dislike picking over 10 integers, which they find inconvenient. Remember, many players buy physical paper tickets.

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