Let n ∈ N. What is the smallest value of k such that every k-subset S of [n] has at least two 2-subsets {a, b} and {c, d} such that |a − b| = |c − d|?
(Here the two 2-subsets must be distinct, but they need not be disjoint

i think it is 18

step-by-step explanation:

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )

step-by-step explanation: