Reciprocal Cycles
A unit fraction contains $1$ in the numerator. The decimal representation of the unit fractions with denominators $2$ to $10$ are given: \begin{align} 1/2 &= 0.5\\ 1/3...
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John Rhodes
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August 15, 2023
$1000$-digit Fibonacci Number
The Fibonacci sequence is defined by the recurrence relation: $F_n = F_{n – 1} + F_{n – 2}$, where $F_1 = 1$ and $F_2 = 1$. Hence...
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John Rhodes
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August 15, 2023
Lexicographic Permutations
A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the...
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John Rhodes
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August 15, 2023
Non-Abundant Sums
A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper...
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John Rhodes
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August 15, 2023
Names Scores
Using names.txt (right click and ‘Save Link/Target As…’), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out...
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John Rhodes
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August 15, 2023
Amicable Numbers
Let $d(n)$ be defined as the sum of proper divisors of $n$ (numbers less than $n$ which divide evenly into $n$). If $d(a) = b$ and $d(b)...
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John Rhodes
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August 15, 2023
Factorial Digit Sum
$n!$ means $n \times (n – 1) \times \cdots \times 3 \times 2 \times 1$. For example, $10! = 10 \times 9 \times \cdots \times 3 \times...
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John Rhodes
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August 15, 2023
Counting Sundays
You are given the following information, but you may prefer to do some research for yourself. 1 Jan 1900 was a Monday. Thirty days has September, April,...