2011 Nines
Consider the real number $\sqrt 2 + \sqrt 3$. When we calculate the even powers of $\sqrt 2 + \sqrt 3$ we get: $(\sqrt 2 + \sqrt...
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John Rhodes
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August 15, 2023
Firecracker
A firecracker explodes at a height of $\pu{100 m}$ above level ground. It breaks into a large number of very small fragments, which move in every direction;...
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John Rhodes
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August 15, 2023
Numbers in Decimal Expansions
Let $p = p_1 p_2 p_3 \cdots$ be an infinite sequence of random digits, selected from $\{0,1,2,3,4,5,6,7,8,9\}$ with equal probability. It can be seen that $p$ corresponds...
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John Rhodes
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August 15, 2023
Digital Root Clocks
Sam and Max are asked to transform two digital clocks into two “digital root” clocks. A digital root clock is a digital clock that calculates digital roots...
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John Rhodes
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August 15, 2023
The Mouse on the Moon
The moon has been opened up, and land can be obtained for free, but there is a catch. You have to build a wall around the land...
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John Rhodes
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August 15, 2023
Sliding Game
In a sliding game a counter may slide horizontally or vertically into an empty space. The objective of the game is to move the red counter from...
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John Rhodes
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August 15, 2023
Biclinic Integral Quadrilaterals
$ABCD$ is a convex, integer sided quadrilateral with $1 \le AB \lt BC \lt CD \lt AD$. $BD$ has integer length. $O$ is the midpoint of $BD$....
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John Rhodes
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August 15, 2023
Nim Square
Alice and Bob play the game Nim Square. Nim Square is just like ordinary three-heap normal play Nim, but the players may only remove a square number...