MathDB
Maximum Number of Elements in a Set

Source:

January 15, 2009

Problem Statement

A subset B B of the set of integers from 1 1 to 100 100, inclusive, has the property that no two elements of B B sum to 125 125. What is the maximum possible number of elements in B B? <spanclass=′latex−bold′>(A)</span> 50<spanclass=′latex−bold′>(B)</span> 51<spanclass=′latex−bold′>(C)</span> 62<spanclass=′latex−bold′>(D)</span> 65<spanclass=′latex−bold′>(E)</span> 68 <span class='latex-bold'>(A)</span>\ 50\qquad <span class='latex-bold'>(B)</span>\ 51\qquad <span class='latex-bold'>(C)</span>\ 62\qquad <span class='latex-bold'>(D)</span>\ 65\qquad <span class='latex-bold'>(E)</span>\ 68
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