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As shown above, a square can be dissected into squares of distinct integer side lengths.
Is it possible to dissect a cube into cubes of distinct integer side lengths?
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Clarification: The number in each square is the side length of that square.
A tennis ball rests directly on top of a cannon ball, which has a much larger mass, i.e. \(M_\textrm{cannonball} \gg M_\textrm{tennis}.\)
When the balls are dropped, to what height (in \(\si{\centi\meter}\)) will the bottom of the tennis ball bounce?
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Details and Assumptions:
\(x\) and \(y\) are positive numbers such that \[\sqrt { xy } \left( x-y \right) =x+y.\] Find the minimum value of \(x+y\) to 2 decimal places.
Let \(S(n)\) be the sum of digits of a positive integer \(n\) (when written in base 10).
If \(S(n) = 4\), find the maximum value of \(S\big(n^4\big)\).
Three circles with equal radii are centered at \((1,0), (0,0),\) and \((0,1)\).
To 4 decimal places, what is the smallest radius of the circles such that we can pick a point within each circle--like A, B, C in the diagram--and connect them to form an equilateral triangle?
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