Sum of Squares II
For a positive integer, $n$, define $g(n)$ to be the maximum perfect square that divides $n$. For example, $g(18) = 9$, $g(19) = 1$. Also define $$\displaystyle...
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John Rhodes
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August 16, 2023
What? Where? When?
“What? Where? When?” is a TV game show in which a team of experts attempt to answer questions. The following is a simplified version of the game....
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John Rhodes
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August 16, 2023
Minimum Area of a Convex Grid Polygon
A symmetrical convex grid polygon is a polygon such that: All its vertices have integer coordinates. All its internal angles are strictly smaller than $180^\circ$. It has...
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John Rhodes
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August 16, 2023
Minimum Area of a Convex Grid Polygon
A symmetrical convex grid polygon is a polygon such that: All its vertices have integer coordinates. All its internal angles are strictly smaller than $180^\circ$. It has...
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John Rhodes
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August 16, 2023
Secret Santa
Secret Santa is a process that allows $n$ people to give each other presents, so that each person gives a single present and receives a single present....
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John Rhodes
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August 16, 2023
Summation of Summations
Take a sequence of length $n$. Discard the first term then make a sequence of the partial summations. Continue to do this over and over until we...
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John Rhodes
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August 16, 2023
Counting Ordered Factorisations
Define $d(n,k)$ to be the number of ways to write $n$ as a product of $k$ ordered integers \[ n = x_1\times x_2\times x_3\times \ldots\times x_k\qquad 1\le...
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John Rhodes
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August 16, 2023
Coin Loops
A game is played with many identical, round coins on a flat table. Consider a line perpendicular to the table. The first coin is placed on the...