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I have a problem in Discrete Math to ask: How many least non-negative numbers are there that we can always take randomly 23 numbers from that set which having sum divisible to 23?

I'm thinking about a set containing all possible remainders when dividing to 23, so the set has 22*23 = 506 numbers. I dont think it is correct, so can you guys help me. Many thanks

Gerry Myerson
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NewbieBoy
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  • Why are your thinking avout such a set? Why don't you think it is correct? Can you please edit your post to share more thoughts and efforts? https://math.stackexchange.com/help/how-to-ask – Anne Bauval Feb 24 '23 at 11:12
  • What do you mean by "we can always take randomly $23$ numbers from that set"? – joriki Feb 24 '23 at 11:42
  • @jor, my guess is OP doesn't really mean random, just that there is a subset of $23$ that add to something divisible by $23$. But maybe you knew that, and just wanted to hear it from OP. – Gerry Myerson Feb 24 '23 at 11:55
  • See https://math.stackexchange.com/questions/3017005/given-n-integers-is-it-always-possible-to-choose-m-from-them-so-that-their and https://math.stackexchange.com/questions/2369377/sum-of-n-numbers-divisible-by-n and https://math.stackexchange.com/questions/807299/prove-that-a-sequence-of-11-numbers-always-contains-six-numbers-summing-up-to – Gerry Myerson Feb 24 '23 at 12:03
  • Have any of those links been helpful, Newbie? – Gerry Myerson Feb 25 '23 at 21:35

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