MathDB
1994 AMC 12 #19

Source:

December 30, 2011
AMC

Problem Statement

Label one disk "11", two disks "22", three disks "33",...,, ..., fifty disks "5050". Put these 1+2+3++50=12751+2+3+ \cdots+50=1275 labeled disks in a box. Disks are then drawn from the box at random without replacement. The minimum number of disks that must be drawn to guarantee drawing at least ten disks with the same label is
<spanclass=latexbold>(A)</span> 10<spanclass=latexbold>(B)</span> 51<spanclass=latexbold>(C)</span> 415<spanclass=latexbold>(D)</span> 451<spanclass=latexbold>(E)</span> 501 <span class='latex-bold'>(A)</span>\ 10 \qquad<span class='latex-bold'>(B)</span>\ 51 \qquad<span class='latex-bold'>(C)</span>\ 415 \qquad<span class='latex-bold'>(D)</span>\ 451 \qquad<span class='latex-bold'>(E)</span>\ 501