Pandigital Multiples
Take the number $192$ and multiply it by each of $1$, $2$, and $3$: \begin{align} 192 \times 1 &= 192\\ 192 \times 2 &= 384\\ 192 \times...
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John Rhodes
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August 15, 2023
Truncatable Primes
The number $3797$ has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage:...
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John Rhodes
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August 15, 2023
Double-base Palindromes
The decimal number, $585 = 1001001001_2$ (binary), is palindromic in both bases. Find the sum of all numbers, less than one million, which are palindromic in base...
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John Rhodes
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August 15, 2023
Circular Primes
The number, $197$, is called a circular prime because all rotations of the digits: $197$, $971$, and $719$, are themselves prime. There are thirteen such primes below...
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John Rhodes
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August 15, 2023
Digit Factorials
$145$ is a curious number, as $1! + 4! + 5! = 1 + 24 + 120 = 145$. Find the sum of all numbers which are...
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John Rhodes
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August 15, 2023
Digit Cancelling Fractions
The fraction $49/98$ is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that $49/98 = 4/8$, which is correct, is...
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John Rhodes
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August 15, 2023
Pandigital Products
We shall say that an $n$-digit number is pandigital if it makes use of all the digits $1$ to $n$ exactly once; for example, the $5$-digit number,...
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John Rhodes
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August 15, 2023
Coin Sums
In the United Kingdom the currency is made up of pound (£) and pence (p). There are eight coins in general circulation: 1p, 2p, 5p, 10p, 20p,...