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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2012 National Olympiad First Round
36
36
Part of
2012 National Olympiad First Round
Problems
(1)
Turkish NMO First Round - 2012 Problem - 36 {Combinatorics}
Source:
7/1/2012
k
k
k
stones are put into
2012
2012
2012
boxes in such a way that each box has at most
20
20
20
stones. We are chosing some of the boxes. We are throwing some of the stones of the chosen boxes. Whatever the first arrangement of the stones inside the boxes is, if we can guarantee that there are equal stones inside the chosen boxes and the sum of them is at least
100
100
100
, then
k
k
k
can be at least?
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420
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349
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296
<span class='latex-bold'>(A)</span>\ 500 \qquad <span class='latex-bold'>(B)</span>\ 450 \qquad <span class='latex-bold'>(C)</span>\ 420 \qquad <span class='latex-bold'>(D)</span>\ 349 \qquad <span class='latex-bold'>(E)</span>\ 296
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450
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420
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349
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296
ceiling function