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Find the smallest value of n from this set?
From the set {1,2,...n}, 11 numbers are removed. Find the smallest value of n, such that no matter those 11 numbers are removed, there always exist at least one Arithmetic progression with length 12?
1 Jawaban
- cryptogramcornerLv 67 tahun yang laluJawaban Favorit
To keep the set as small as possible, I think we will want the arithmetic progression to have a common
difference of 1, and would consist of 12 consective integers. So now we must think of the worst possible
case of preventing consective runs of integers. if you picked 12, 24, 36, etc, you would prevent
runs of twelve from occuring all the way up to n = 11 x 12 + 11 = 143
With 144, you'd be able to make a run of 12.
