In my experience there are no impolite numbers
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The only impolite numbers are powers of two. Since 544 cannot be formed by an integer power of 2, it is polite.
Could you generate a complete set of 6 number combinations from 45 numbers ?
Cluster Sampling
2,3,5,7,9,11,13,17,19,23,29,31,37,39,41,43,47,49
subtract the smallest one