Expert Solutions | Senioritis

John Rhodes
August 15, 2023
Computational Mathematics

At Least Four Distinct Prime Factors Less Than 100

It can be verified that there are $23$ positive integers less than $1000$ that are divisible by at least four distinct primes less than $100$. Find how...

John Rhodes
August 15, 2023
Computational Mathematics

Billionaire

You are given a unique investment opportunity. Starting with £1 of capital, you can choose a fixed proportion, f, of your capital to bet on a fair...

John Rhodes
August 15, 2023
Computational Mathematics

Pseudo Square Root

The divisors of $12$ are: $1,2,3,4,6$ and $12$. The largest divisor of $12$ that does not exceed the square root of $12$ is $3$. We shall call...

John Rhodes
August 15, 2023
Computational Mathematics

Binary Circles

$2^N$ binary digits can be placed in a circle so that all the $N$-digit clockwise subsequences are distinct. For $N=3$, two such circular arrangements are possible, ignoring...

John Rhodes
August 15, 2023
Computational Mathematics

Consider all the triangles having: All their vertices on lattice pointsInteger coordinates. CircumcentreCentre of the circumscribed circle at the origin $O$. OrthocentrePoint where the three altitudes meet...

John Rhodes
August 15, 2023
Computational Mathematics

An Engineers’ Dream Come True

Consider the number $6$. The divisors of $6$ are: $1,2,3$ and $6$. Every number from $1$ up to and including $6$ can be written as a sum...

John Rhodes
August 15, 2023
Computational Mathematics

Mountain Range

The following equation represents the continuous topography of a mountainous region, giving the elevationheight above sea level $h$ at any point $(x, y)$: $$h = \left(5000 –...

John Rhodes
August 15, 2023
Computational Mathematics

Pivotal Square Sums

Let us call a positive integer $k$ a square-pivot, if there is a pair of integers $m \gt 0$ and $n \ge k$, such that the sum...