Sub-string Divisibility
The number, $1406357289$, is a $0$ to $9$ pandigital number because it is made up of each of the digits $0$ to $9$ in some order, but...
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John Rhodes
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August 15, 2023
Coded Triangle Numbers
The $n$th term of the sequence of triangle numbers is given by, $t_n = \frac12n(n+1)$; so the first ten triangle numbers are: $$1, 3, 6, 10, 15,...
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John Rhodes
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August 15, 2023
Pandigital Prime
We shall say that an $n$-digit number is pandigital if it makes use of all the digits $1$ to $n$ exactly once. For example, $2143$ is a...
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John Rhodes
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August 15, 2023
Champernowne’s Constant
An irrational decimal fraction is created by concatenating the positive integers: $$0.12345678910{\color{red}\mathbf 1}112131415161718192021\cdots$$ It can be seen that the $12$th digit of the fractional part is $1$....
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John Rhodes
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August 15, 2023
Integer Right Triangles
If $p$ is the perimeter of a right angle triangle with integral length sides, $\{a, b, c\}$, there are exactly three solutions for $p = 120$. $\{20,48,52\}$,...
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John Rhodes
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August 15, 2023
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...