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Let-S-1-2-3-4-48-49-What-is-the-maximum-value-of-n-such-that-it-is-possible-to-select-n-numbers-from-S-and-arrange-them-in-a-circle-in-such-a-way-that-the-product-of-any-two-adjacent-numbers




Question Number 116356 by bemath last updated on 03/Oct/20
Let S ={1,2,3,4,...,48,49} .What is  the maximum value of n such that  it is possible to select n numbers   from S and arrange them in a circle   in such a way that the product of  any two adjacent numbers in the  circle is less than 100?
$$\mathrm{Let}\:\mathrm{S}\:=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},…,\mathrm{48},\mathrm{49}\right\}\:.\mathrm{What}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{select}\:\mathrm{n}\:\mathrm{numbers}\: \\ $$$$\mathrm{from}\:\mathrm{S}\:\mathrm{and}\:\mathrm{arrange}\:\mathrm{them}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\: \\ $$$$\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of} \\ $$$$\mathrm{any}\:\mathrm{two}\:\mathrm{adjacent}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{circle}\:\mathrm{is}\:\mathrm{less}\:\mathrm{than}\:\mathrm{100}? \\ $$

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