Problem 53990. Classify product/digitsum sequences
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I didn't find a key, but a predominance between the five lists: 9 is the most powerful. 4 or 5 tests are enough, but some have made matrices with more than 25 possible combinations.
Tip FYI: If the sum of the digits of a number is divisible by 3, then the number is also divisible by 3, and the same rule exists for 9. All numbers have similar laws, it seems. A number divisible by 5 ends with 0 or 5, and so on...
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