Chess Sliders
A Slider is a chess piece that can move one square left or right. This problem uses a cylindrical chess board where the left hand edge of...
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John Rhodes
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August 16, 2023
Factor Shuffle
A list initially contains the numbers $2, 3, \dots, n$. At each round, every number in the list is divided by its smallest prime factor. Then the...
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John Rhodes
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August 16, 2023
Square the Smallest
A list initially contains the numbers $2, 3, \dots, n$. At each round, the smallest number in the list is replaced by its square. If there is...
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John Rhodes
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August 16, 2023
123-Separable
A set, $S$, of integers is called 123-separable if $S$, $2S$ and $3S$ are disjoint. Here $2S$ and $3S$ are obtained by multiplying all the elements in...
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John Rhodes
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August 16, 2023
$N$th Digit of Reciprocals
Let $d_n(x)$ be the $n$th decimal digit of the fractional part of $x$, or $0$ if the fractional part has fewer than $n$ digits. For example: $d_7...
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John Rhodes
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August 16, 2023
Iterative Sampling
Given an $n$-tuple of numbers another $n$-tuple is created where each element of the new $n$-tuple is chosen randomly from the numbers in the previous $n$-tuple. For...
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John Rhodes
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August 16, 2023
SET
The SET® card game is played with a pack of $81$ distinct cards. Each card has four features (Shape, Color, Number, Shading). Each feature has three different...
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John Rhodes
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August 16, 2023
Digits in Squares
Define $m = M(n, d)$ to be the smallest positive integer such that when $m^2$ is written in base $n$ it includes the base $n$ digit $d$....