Computational Mathematics

John Rhodes
August 15, 2023
Computational Mathematics

Phigital Number Base

Let $\varphi$ be the golden ratio: $\varphi=\frac{1+\sqrt{5}}{2}.$ Remarkably it is possible to write every positive integer as a sum of powers of $\varphi$ even if we require...

John Rhodes
August 15, 2023
Computational Mathematics

Comfortable Distance II

There are $N$ seats in a row. $N$ people come one after another to fill the seats according to the following rules: No person sits beside another....

John Rhodes
August 15, 2023
Computational Mathematics

Triangle Inscribed in Ellipse

The triangle $\triangle ABC$ is inscribed in an ellipse with equation $\frac {x^2} {a^2} + \frac {y^2} {b^2} = 1$, $0 \lt 2b \lt a$, $a$ and...

John Rhodes
August 15, 2023
Computational Mathematics

Super Ramvok

Consider a single game of Ramvok: Let $t$ represent the maximum number of turns the game lasts. If $t = 0$, then the game ends immediately. Otherwise,...

John Rhodes
August 15, 2023
Computational Mathematics

Empty Chairs

In a room $N$ chairs are placed around a round table. Knights enter the room one by one and choose at random an available empty chair. To...

John Rhodes
August 15, 2023
Computational Mathematics

Smooth Divisors of Binomial Coefficients

An integer is called B-smooth if none of its prime factors is greater than $B$. Let $S_B(n)$ be the largest $B$-smooth divisor of $n$. Examples: $S_1(10)=1$ $S_4(2100)...

John Rhodes
August 15, 2023
Computational Mathematics

Superinteger

An integer $s$ is called a superinteger of another integer $n$ if the digits of $n$ form a subsequenceA subsequence is a sequence that can be derived...

John Rhodes
August 15, 2023
Computational Mathematics

Distinct Terms in a Multiplication Table

Let $P(m,n)$ be the number of distinct terms in an $m\times n$ multiplication table. For example, a $3\times 4$ multiplication table looks like this: $\times$ 12341 12342...