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,...
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John Rhodes
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August 15, 2023
Maximum Path Sum I
By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23....
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John Rhodes
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August 15, 2023
Number Letter Counts
If the numbers $1$ to $5$ are written out in words: one, two, three, four, five, then there are $3 + 3 + 5 + 4 +...
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John Rhodes
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August 15, 2023
Power Digit Sum
$2^{15} = 32768$ and the sum of its digits is $3 + 2 + 7 + 6 + 8 = 26$. What is the sum of the...
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John Rhodes
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August 15, 2023
Lattice Paths
Starting in the top left corner of a $2 \times 2$ grid, and only being able to move to the right and down, there are exactly $6$...
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John Rhodes
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August 15, 2023
Longest Collatz Sequence
The following iterative sequence is defined for the set of positive integers: $n \to n/2$ ($n$ is even) $n \to 3n + 1$ ($n$ is odd) Using...