Sliding Game
In a sliding game a counter may slide horizontally or vertically into an empty space. The objective of the game is to move the red counter from...
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John Rhodes
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August 15, 2023
Biclinic Integral Quadrilaterals
$ABCD$ is a convex, integer sided quadrilateral with $1 \le AB \lt BC \lt CD \lt AD$. $BD$ has integer length. $O$ is the midpoint of $BD$....
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John Rhodes
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August 15, 2023
Nim Square
Alice and Bob play the game Nim Square. Nim Square is just like ordinary three-heap normal play Nim, but the players may only remove a square number...
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John Rhodes
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August 15, 2023
Integer Ladders
In the classic “Crossing Ladders” problem, we are given the lengths $x$ and $y$ of two ladders resting on the opposite walls of a narrow, level street....
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John Rhodes
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August 15, 2023
An Amazing Prime-generating Automaton
A program written in the programming language Fractran consists of a list of fractions. The internal state of the Fractran Virtual Machine is a positive integer, which...
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John Rhodes
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August 15, 2023
Chip Defects
$k$ defects are randomly distributed amongst $n$ integrated-circuit chips produced by a factory (any number of defects may be found on a chip and each defect is...
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John Rhodes
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August 15, 2023
Paper-strip Game
The following game is a classic example of Combinatorial Game Theory: Two players start with a strip of $n$ white squares and they take alternate turns. On...
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John Rhodes
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August 15, 2023
Reflexive Position
Let’s call $S$ the (infinite) string that is made by concatenating the consecutive positive integers (starting from $1$) written down in base $10$. Thus, $S = 1234567891011121314151617181920212223242\cdots$...