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...

1 year 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...

1 year ago

Solved

Mesh the square with triangles
Problem statement An square is a regular polygon with 4 vertices and 4 edges. Here below is an example of the vertex set V, c...

1 year 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,...

1 year 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...

1 year 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...

1 year 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...

1 year 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 ...

1 year 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...

1 year 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...

1 year ago

Solved

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...

1 year ago

Solved

Evaluate Deterministic Finite Automata on String
Given a Deterministic Finite Automata (DFA) and a string, determine whether or not the DFA will accept when ran on the string. A...

1 year ago

Solved

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 : ...

1 year 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...

1 year 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 ...

1 year ago

Solved

Determine if LTI system with feedback control is stable
Linear timeiinvariant systems can be represented by the differential equation , where is an matrix, is an vector representing...

1 year 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...

1 year 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...

1 year ago

Solved

Determine whether a number is a seesaw number
Cody Problem 60957 dealt with balanced primes. In that case, balance was measured in terms of the average of primes around a giv...

1 year ago

Solved

List mean-of-2 primes
The prime number 53 is the average of the first prime before it (47) and the first prime after it (59), and the prime number 11 ...

1 year ago

Solved

Chek the Delta = 6k gap conjecture 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...

1 year ago

Solved

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

1 year ago

Solved

Compile evidence for the Carmichael totient conjecture
The totient function counts the positive integers up to that are relatively prime to . The Carmichael totient conjecture state...

1 year ago

Solved

Find the longest runs of primes generated by polynomials
Cody Problems 60942, 60943, and 60944 involve polynomials that generate primes. No polynomial can generate only prime numbers, b...

1 year ago

Solved

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

1 year ago

Solved

Check the 'golden prime squares' equation
Historical context In december 2023, I / Nicolas Douillet was working on prime squares properties and I found* the formula : ...

1 year 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 ...

1 year ago

Solved

Fermat primes
Historical context The french mathematician Pierre de Fermat found the formula to find some prime numbers. He thought / co...

1 year 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 ...

1 year ago

Solved

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

1 year ago