Nim
Nim is a game played with heaps of stones, where two players take it in turn to remove any number of stones from any heap until no...
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John Rhodes
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August 15, 2023
Protein Folding
In a very simplified form, we can consider proteins as strings consisting of hydrophobic (H) and polar (P) elements, e.g. HHPPHHHPHHPH. For this problem, the orientation of...
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John Rhodes
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August 15, 2023
Three Similar Triangles
Four points with integer coordinates are selected:$A(a, 0)$, $B(b, 0)$, $C(0, c)$ and $D(0, d)$, with $0 \lt a \lt b$ and $0 \lt c \lt d$....
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John Rhodes
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August 15, 2023
Selective Amnesia
Larry and Robin play a memory game involving a sequence of random numbers between 1 and 10, inclusive, that are called out one at a time. Each...
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John Rhodes
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August 15, 2023
Zeckendorf Representation
Each new term in the Fibonacci sequence is generated by adding the previous two terms. Starting with $1$ and $2$, the first $10$ terms will be: $1,...
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John Rhodes
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August 15, 2023
Angular Bisector and Tangent
Given is an integer sided triangle $ABC$ with $BC \le AC \le AB$.$k$ is the angular bisector of angle $ACB$.$m$ is the tangent at $C$ to the...
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John Rhodes
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August 15, 2023
Lenticular Holes
We call the convex area enclosed by two circles a lenticular hole if: The centres of both circles are on lattice points. The two circles intersect at...
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John Rhodes
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August 15, 2023
Pseudo-Fortunate Numbers
An even positive integer $N$ will be called admissible, if it is a power of $2$ or its distinct prime factors are consecutive primes. The first twelve...