Special Subset Sums: Optimum
Let $S(A)$ represent the sum of elements in set $A$ of size $n$. We shall call it a special sum set if for any two non-empty disjoint...
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John Rhodes
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August 15, 2023
Triangle Containment
Three distinct points are plotted at random on a Cartesian plane, for which $-1000 \le x, y \le 1000$, such that a triangle is formed. Consider the...
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John Rhodes
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August 15, 2023
Optimum Polynomial
If we are presented with the first $k$ terms of a sequence it is impossible to say with certainty the value of the next term, as there...
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John Rhodes
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August 15, 2023
Arranged Probability
If a box contains twenty-one coloured discs, composed of fifteen blue discs and six red discs, and two discs were taken at random, it can be seen...
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John Rhodes
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August 15, 2023
Largest Exponential
Comparing two numbers written in index form like $2^{11}$ and $3^7$ is not difficult, as any calculator would confirm that $2^{11} = 2048 \lt 3^7 = 2187$....
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John Rhodes
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August 15, 2023
Anagramic Squares
By replacing each of the letters in the word CARE with $1$, $2$, $9$, and $6$ respectively, we form a square number: $1296 = 36^2$. What is...
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John Rhodes
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August 15, 2023
Large Non-Mersenne Prime
The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form $2^{6972593} – 1$; it contains...
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John Rhodes
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August 15, 2023
Su Doku
Su Doku (Japanese meaning number place) is the name given to a popular puzzle concept. Its origin is unclear, but credit must be attributed to Leonhard Euler...