This week’s Fiddler is about rounding! Let $\text{round}(x)$ be the value of $x$ rounded to the nearest integer. Suppose $x_1,\dots,x_n$ are independent uniformly distributed random variables in $[0,1]$. Find the probability that \[ \text{round}(x_1+\cdots+x_n) = \text{round}(x_1)+\cdots+\text{round}(x_n) \] My solution: [Show Solution] Let’s call the probability we seek $p(n)$. The values of the $x_i$ determine what … Continue reading "Round, round, get a round" The post Round, round, ...| Book Proofs
This week’s Fiddler is a challenging counting problem. Consider the following array of 25 squares: You are filling the array with rectangles by repeating the following two steps: Select one of the 12 squares along the outer perimeter that has not yet been selected as part of a rectangle. Form the largest rectangle you can … Continue reading "Tiling a Tilted Square" The post Tiling a Tilted Square first appeared on Book Proofs.| Book Proofs
One important element when working with mathematics is fractions. We are taught to use fractions in school, but their presence is constant throughout all fields of mathematics and sciences. Writing fractions inside a LaTeX document is straightforward: you just have to use the frac{}{} command in math mode:| LaTeX-Tutorial.com