MathDB

35

Part of 2000 National Olympiad First Round

Problems(1)

Turkish NMO First Round - 2000 P-35 (Combinatorics)

Source:

7/8/2012
If every k−k-element subset of S={1,2,…,32}S=\{1,2,\dots , 32\} contains three different elements a,b,ca,b,c such that aa divides bb, and bb divides cc, kk must be at least ?
<spanclass=′latex−bold′>(A)</span> 17<spanclass=′latex−bold′>(B)</span> 24<spanclass=′latex−bold′>(C)</span> 25<spanclass=′latex−bold′>(D)</span> 29<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ 17 \qquad<span class='latex-bold'>(B)</span>\ 24 \qquad<span class='latex-bold'>(C)</span>\ 25 \qquad<span class='latex-bold'>(D)</span>\ 29 \qquad<span class='latex-bold'>(E)</span>\ \text{None}