+8 +8 +4 +1911 +1911 +1911 +1911 +180 +1911 +1911 +1678 +4 +1678 +1348 Let the ordered triples $(x,y,z)$ of complex numbers that satisfy
\begin{align*}
x + yz &= 7, \\
y + xz &= -3, \\
z + xy &= -5.<#> \end{align*}<#> be $(x_1,y_1,z_1),$ $(x_2,y_2,z_2),$ $\dots,$ $(x_n,y_n,z_n).$
read more .. +1348 +1348 Oct 26, 2023
+1911 In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers ($1,$ $2,$ $3,$ $4,$ $5,$ $6,$ and $7$). Among all the cards of each color, there is exactly one card labeled with each number.
read more .. +1911 +1911 Sam writes down the numbers $1,$ $2,$ $\dots,$ $315,$ $316,$ $317,$ $\dots,$ $248,$ $249,$ $250.$
(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down at random. What is the probability
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