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Mesh the icosahedron
Problem statement An icosahedron is a regular polyhedron with 12 vertices and 20 triangular faces. It is also one of the five...

6 months ago

Solved

Mesh the dodecahedron
Problem statement An dodecahedron is a regular polyhedron with 20 vertices and 12 pentagonal faces. It is also one of the fiv...

6 months ago

Solved

Build triangulation from -sorted- edge list
Problem statement An edge list is simply a N x 2 matrix of positive integers, in which N is the number of edges and each intege...

6 months ago

Solved

Check Euler's characteristic on regular polyhedra
Problem statement Given the number of vertices and the number of faces of a given regular polyhedron, compute the number of its...

6 months ago

Solved

Mesh the square with triangles
Problem statement An square is a regular polygon with 4 vertices and 4 edges. A triangulated mesh T (stands for triangles he...

6 months ago

Solved

Pitting corrosion on a metal plate: Count the number of pits
You are given an N x M matrix of _ones_ and _zeros_, which represents an image of a rectangular metal plate taken from the hull ...

6 months ago

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Identify Ruth-Aaron numbers
After Hank Aaron hit his 715th home run and passed Babe Ruth’s total of 714, Carl Pomerance noticed that the union of the prime ...

6 months ago

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(Linear) Recurrence Equations - Generalised Fibonacci-like sequences
This problem is inspired by problems <http://uk.mathworks.com/matlabcentral/cody/problems/2187-generalized-fibonacci 2187>, <htt...

6 months ago

Solved

Mesh the pentagon (with the minimum number of triangles)
Problem statement An pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set V,...

6 months ago

Solved

Mesh the tetrahedron
Problem statement An tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five w...

6 months ago

Solved

Mesh the cube
Problem statement : mesh the cube with quadranglar / squared faces An cube / regular hexahedron is a regular polyhedron with ...

6 months ago

Solved

Mesh the octahedron
Problem statement An octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five we...

6 months ago

Solved

Linear primes p' = mp + n
Problem statement List the prime numbers of the form p' = mp + n for a given (m,n) couple and such that p' < k, k positive in...

6 months ago

Solved

List the complementary / symetric prime couples
Problem statement For a given positive integer n, provide the prime couples (p,p') such that p + p' = 10^n. NB : a number li...

6 months ago

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Check Legendre's conjecture
Context and problem statement Legendre's conjecture states for a given positive integer n, there always exists at least one pri...

6 months ago

Solved

List the twin prime couples
Problem statement The twin prime couples (p,p') are the ones such that p' = p + 2. For a given integer n > 1, list the twin p...

6 months ago

Solved

Check Bertrand-Chebyshev's theorem about prime numbers
Historical context Bertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory ...

6 months ago

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Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3
Problem statement For all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 : ...

6 months ago

Solved

Check p = 4n +/- 1, the generic formula for odd prime numbers
Problem statement For all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 : Check this f...

6 months ago

Solved

List even numbers whose Goldbach partition does not use the largest prime
The strong Goldbach conjecture says that every even number greater than 2 can be expressed as a sum of two prime numbers—that is...

6 months ago

Solved

Monkey and the Peaches
A monkey picked a certain number of peaches on the first day. Each day, the monkey eats half of the remaining peaches plus one ...

6 months ago

Solved

List primes which are the sum of two consecutive lower primes plus minus one
Problem statement Some prime numbers can be written as the sum of two consecutive lower primes plus / minus one : Like t...

6 months ago

Solved

List the near-square primes, p = n² + 1 (Landau's 4th problem)
Historical context At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime...

6 months ago

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Chek the Delta = p' - p = 6k gap theorem about arithmetic progressions in the prime number set
Context In the prime numbers set there are some arithmetic progressions (sequences of three or more consecutive prime number...

6 months ago

Solved

P(girl likes you | she smiled at you)
Compute the probability Given the input probabilities

6 months ago

Solved

My wife's logic
Its is always the opposite of the causality law, that is to say the opposite of the implication relationship in math/logic terms...

6 months ago

Solved

Extra colors
Context In the RGB color system used by Matlab, the color is a 1 x 3 / row vector [R G B] with each value/component R, G, B in ...

6 months ago

Solved

Check the integers additive decomposition conjecture
Problem statement A conjecture (I rediscovered ?) related to Goldbach's one states that every integer above 2 can be written ...

6 months ago

Solved

Check p² = 24k + 1, p > 3, the 'golden prime squares' equation
Historical context In december 2023, I / Nicolas Douillet was working on prime squares properties and I found* the formula : ...

6 months ago

Solved

Euclid primes
Historical context Euclid, the greek mathematician proved at his time that the prime numbers set is an infinite. By the way he ...

6 months ago