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SMO 2010 Open Round 1 Question 23

SMO · SMO 2010 Open Round 1

Question 23

All six-digit numbers whose digits occur from left to right in non-increasing order, for example $966541$, are listed in increasing numerical order. The first three are $100000,110000,111000$. If the $2010$th number is $p$, find $\lfloor p/10\rfloor$, where $\lfloor x\rfloor$ is the greatest integer not exceeding $x$.