The King’s Banquet
The Knights of the Order of Fibonacci are preparing a grand feast for their king. There are $n$ knights, and each knight is assigned a distinct number...
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John Rhodes
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August 16, 2023
Square Root Smooth Numbers
A positive integer is called square root smooth if all of its prime factors are strictly less than its square root. Including the number $1$, there are...
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John Rhodes
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August 16, 2023
Moving Pentagon
After buying a Gerver Sofa from the Moving Sofa Company, Jack wants to buy a matching cocktail table from the same company. Most important for him is...
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John Rhodes
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August 16, 2023
Polymorphic Bacteria
Members of a species of bacteria occur in two different types: $\alpha$ and $\beta$. Individual bacteria are capable of multiplying and mutating between the types according to...
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John Rhodes
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August 16, 2023
Proportionate Nim
Two players play a game with two piles of stones, alternating turns. On each turn, the corresponding player chooses a positive integer $n$ and does one of...
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John Rhodes
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August 16, 2023
An Infinite Game
Peter is playing a solitaire game on an infinite checkerboard, each square of which can hold an unlimited number of tokens. Each move of the game consists...
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John Rhodes
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August 16, 2023
Sums of Subarrays
Let $t_k$ be the tribonacci numbers defined as: $\quad t_0 = t_1 = 0$; $\quad t_2 = 1$; $\quad t_k = t_{k-1} + t_{k-2} + t_{k-3} \quad...
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John Rhodes
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August 16, 2023
Fibonacci Paths
Alice walks on a lattice grid. She can step from one lattice point $A (a,b)$ to another $B (a+x,b+y)$ providing distance $AB = \sqrt{x^2+y^2}$ is a Fibonacci...