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I thought of this last night, not sure if this has a solution. More likely someone else already did it under a name I couldn't find. What do you ...

\[ \large 100 \lim_{n \to \infty} \sum_{k=1}^{\left \lfloor \frac{n-\sqrt{n}}{2} \right \rfloor} \frac{\binom{50n}{k}\binom{50n}{n-k}}{\binom{100n}{n}} = \, ? \]

Find the ratio of the areas of the smallest square to the largest square.

Note:

-In each quarter circle, the squares inscribed in it are elevated \(45^{\circ}\) from the ...

My favorite integer is divisible by 6, 7, 8, and 9.

Then my favorite integer must also be divisible by which of the following numbers?

\[ x^2 + {\Large\square} = 10x \]

If \(x\) is a positive integer, how many ways are there to fill in the blank with a positive number?

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