John Rhodes, Math Teacher at Senioritis.io

John Rhodes
August 16, 2023
Computational Mathematics

Concatenation Coincidence

A non-decreasing sequence of integers $a_n$ can be generated from any positive real value $\theta$ by the following procedure: \begin{align} \begin{split} b_1 &= \theta \\ b_n &=...

John Rhodes
August 16, 2023
Computational Mathematics

Optimal Card Stacking

Card Stacking is a game on a computer starting with an array of $N$ cards labelled $1,2,\ldots,N$. A stack of cards can be moved by dragging horizontally...

John Rhodes
August 16, 2023
Computational Mathematics

Near Power Sums

A positive integer, $n$, is a near power sum if there exists a positive integer, $k$, such that the sum of the $k$th powers of the digits...

John Rhodes
August 16, 2023
Computational Mathematics

Triangular Pizza

Mamma Triangolo baked a triangular pizza. She wants to cut the pizza into $n$ pieces. She first chooses a point $P$ in the interior (not boundary) of...

John Rhodes
August 16, 2023
Computational Mathematics

A Messy Dinner

$n$ families, each with four members, a father, a mother, a son and a daughter, were invited to a restaurant. They were all seated at a large...

John Rhodes
August 16, 2023
Computational Mathematics

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...

John Rhodes
August 16, 2023
Computational Mathematics

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....

John Rhodes
August 16, 2023
Computational Mathematics

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...