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...
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John Rhodes
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August 15, 2023
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...
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John Rhodes
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August 15, 2023
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...
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John Rhodes
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August 15, 2023
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 +...
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John Rhodes
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August 15, 2023
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....
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John Rhodes
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August 15, 2023
Combinatoric Selections
There are exactly ten ways of selecting three from five, 12345: 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345 In combinatorics, we use the...
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John Rhodes
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August 15, 2023
Permuted Multiples
It can be seen that the number, $125874$, and its double, $251748$, contain exactly the same digits, but in a different order. Find the smallest positive integer,...
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John Rhodes
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August 15, 2023
Prime Digit Replacements
By replacing the 1st digit of the 2-digit number *3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83,...