Expert Solutions | Senioritis

John Rhodes
August 15, 2023
Computational Mathematics

Cyclical Figurate Numbers

Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae: Triangle $P_{3,n}=n(n+1)/2$ $1, 3, 6,...

John Rhodes
August 15, 2023
Computational Mathematics

Prime Pair Sets

The primes $3$, $7$, $109$, and $673$, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime....

John Rhodes
August 15, 2023
Computational Mathematics

XOR Decryption

Each character on a computer is assigned a unique code and the preferred standard is ASCII (American Standard Code for Information Interchange). For example, uppercase A =...

John Rhodes
August 15, 2023
Computational Mathematics

Spiral Primes

Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed. 37 36 35 34 33 32 31 38...

John Rhodes
August 15, 2023
Computational Mathematics

Square Root Convergents

It is possible to show that the square root of two can be expressed as an infinite continued fraction. $\sqrt 2 =1+ \frac 1 {2+ \frac 1...

John Rhodes
August 15, 2023
Computational Mathematics

Powerful Digit Sum

A googol ($10^{100}$) is a massive number: one followed by one-hundred zeros; $100^{100}$ is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum...

John Rhodes
August 15, 2023
Computational Mathematics

Lychrel Numbers

If we take $47$, reverse and add, $47 + 74 = 121$, which is palindromic. Not all numbers produce palindromes so quickly. For example, \begin{align} 349 +...

John Rhodes
August 15, 2023
Computational Mathematics

Poker Hands

In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way: High Card: Highest value card....