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Problem of the Day #4: Exponentiated Factorial March 23, 2011

Posted by Albert in : potd , add a comment

Determine the last three non-zero digits of $(20!)^{2000}$

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Problem of the Day #3: Minimum Possible Triangle Perimeter March 22, 2011

Posted by Alex in : potd , add a comment

A circle with center $C$ passes through point $B$. Let $A$ be a point outside of the circle and $Q$ be the intersection of the circle and $\overline{AB}$. If $\angle ACB$ is a right angle and $\overline{AB}$, $\overline{AC}$, $\overline{BC}$, and $\overline{BQ}$ have integer lengths, find the minimum possible perimeter of $\triangle CBQ$.

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Problem of the Day #2: Time taken to reach a spider March 21, 2011

Posted by Sreenath in : potd , add a comment

Seungln is standing two feet away from a spider. He takes a one-foot step once a second, either forwards (toward the spider) with $\frac57$ probability or backwards with $\frac27$ probability. Compute the expected value of the time it takes Seungln to reach the spider.

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A Two-Player Board Game March 20, 2011

Posted by Saketh in : bonus , add a comment

On a 5×5 board, two players, Albert and Billy, alternately mark numbers on empty cells. The first player, Albert, always marks 1′s, the second, Billy, 0′s. One number is marked per turn, until the board is filled. For each of the nine 3 x 3 squares the sum of the nine numbers on its cells is computed. How large can the Albert force the maximum of these sums to be regardless of Billy’s behavior?

Problem of the Day #1: 15 heads or 14 tails March 20, 2011

Posted by Saketh in : potd , add a comment

Albert is flipping his lucky coin, keeping track of the cumulative number of heads and tails. If the probability that he reaches $15$ heads before he reaches $14$ tails is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, find the remainder when $m+n$ is divided by $1000$.

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