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--- pow:problem5f20 [2020/11/10 03:49] – created mazur
+++ pow:problem5f20 [2020/11/10 03:54] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 80% round orange|Problem 5 (due Monday, November 9)>
+Recall that $\lfloor a \rfloor$ denotes the floor of $a$, i.e. the largest integer smaller or equal than $a$.
+What is the smallest possible value of $\displaystyle \left\lfloor \frac{1}{x_1}\right\rfloor+\left\lfloor\frac{1}{x_2}\right\rfloor+\ldots +\left \lfloor\frac{1}{x_n}
+\right\rfloor$, where $x_1,x_2,\ldots, x_n$ are positive real numbers such that $x_1+\ldots +x_n=1$?
+ </box>
+Yuqiao Huang is the only person who submitted a solution. His solution is very nice and it is
+based on a different idea than our solution. Both solutions are discussed in the following link {{:pow:2020fproblem5.pdf|Solution}}