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P06 [Number Theory] - Turkish NMO 1st Round - 2003

Source:

May 9, 2014
floor function

Problem Statement

How many 00s are there at the end of the decimal representation of 2000!2000!?
<spanclass=′latex−bold′>(A)</span> 222<spanclass=′latex−bold′>(B)</span> 499<spanclass=′latex−bold′>(C)</span> 625<spanclass=′latex−bold′>(D)</span> 999<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 222 \qquad<span class='latex-bold'>(B)</span>\ 499 \qquad<span class='latex-bold'>(C)</span>\ 625 \qquad<span class='latex-bold'>(D)</span>\ 999 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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