<img align="right" src="http://plg1.cs.uwaterloo.ca/%7Eacm00/091003/E.png" alt="" /> <p>An evil professor has just assigned you the following problem.</p> <p>A sequence is defined by the following recurrence:</p> <p><img …

<p>A polygon is lowered at a constant speed of <i>v</i> metres per minute from the air into a liquid that dissolves it at a constant speed of <i>c</i> metres per minute from all sides. Given a point <i>(x,y)</i> inside…

<p><img src="http://acm.zj.cn/upload/2010/3/B-22104525.jpg" alt="" /></p> <p>After writing a solver for the &quot;moveable maze&quot; game last week, you have grown tired of it. After all, you already know the optimal solution. …

<p>&nbsp;</p> <p>The ternary expansion of a number is that number written in base 3. A number can have more than one ternary expansion. A ternary expansion is indicated with a subscript 3. For example, 1 = 1₃ = 0.22…

<p>A Benedict monk No. 16 writes down the decimal representations of all natural numbers between and including</p> <p><b>m and</b> <b>n , m<b>&le;</b> n</b></p> <p>. How many 0's will he wri…

<p>You have unexpectedly become the owner of a large chessboard, having fifteen squares to each side. Because you do not know how to play chess on such a large board, you find an alternative way to make use of it.</p> <p>In chess, a rook atta…