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 ...

3 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...

3 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...

3 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...

3 months 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 : ...

3 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...

3 months ago

Solved

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...

3 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...

3 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...

3 months ago

Solved

Convex Hull Capture
Imagine four points in uv that form a square. uv = [ ... 0,0; 0,2; 2,2; 2,0]; Now we have two more po...

3 months ago

Solved

Minimal cost
A power house, P, is on one bank of a straight river W meters wide, and a factory, F, is on the opposite bank L meters downstrea...

3 months ago

Solved

Next Lower Power of B
Given a number _n_ and a base _B_ greater than 1, return the lowest integer power of _B_ that is less than or equal to _n_. E...

3 months ago

Solved

Find the definite integral of various linear functions
A definite integral had a minimum and maximum limit. When you solve this type of problem you must use both quad and the trapz fu...

3 months ago

Solved

Find the "ordinary" or Euclidean distance between A and Z
A, B and Z define three points in the 3D _Euclidean_ space of the form: A = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z]; Find th...

3 months ago

Solved

Sort numbers by outside digits
Sort the array so that they are sorted as if their value was a 5 digit number made from the first three and last two digits of t...

3 months ago

Solved

What is the next step in Conway's Life?
Given a matrix A that represents the state of Conway's game of Life at one instant (time t=n), return the matrix B that represen...

3 months ago

Solved

Spiral In
Create an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the ...

3 months ago

Solved

DNA N-Gram Distribution
Given a string s and a number n, find the most frequently occurring n-gram in the string, where the n-grams can begin at any poi...

3 months ago

Solved

Times 2 - START HERE
Try out this test problem first. Given the variable x as your input, multiply it by two and put the result in y. Examples:...

3 months ago

Solved

Relative points in 2D: problem 1
The 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T. A lan...

3 months ago

Solved

Relative pose in 2D: problem 2
We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north. There is a ...

3 months ago

Solved

Wind Chill Computation
On a windy day, a temperature of 15 degrees may feel colder, perhaps 7 degrees. The formula below calculates the "wind chill," i...

3 months ago

Solved

Clueless - Lord Ned in the Game Room with the Technical Computing Language
[Warning: this is a nontrivial programming problem] Worried about the decline in reasoning skills in the clueless populace of...

3 months ago

Solved

Popular Word Game™ Distance
Professor Ned, who holds the Nedowed Chair of Crackpot Mathematics at the University of Nedsburg, has recently discovered the da...

3 months ago

Solved

The Bridges of Nedsburg
The fabled city of Nedsburg consists of several islands connected by bridges. Due to tectonic forces, shoddy civil engineering, ...

3 months ago

Solved

A Nedlish Country Garden - Check for Valid Arrangement
Nedland is famous for its stately gardens, which typically have a centerpiece of a square grid, with certain squares featuring a...

3 months ago

Solved

Average Number of Moves for the Royal Game of Err
Bored of tedious court assemblies, King Neduchadneddar the Procrastinator has found a cunning way to keep his advisors, councilo...

3 months ago

Solved

Convert Decimal to Hexavigesimal
NASA (Ned’s Alien-Spying Agency) have made contact with a 13-fingered race from the planet Genai. Naturally, Ned’s shadowy opera...

3 months ago

Solved

Transition Matrix for the Royal Game of Err
Bored of tedious court assemblies, King Neduchadneddar the Procrastinator has found a cunning way to keep his advisors, councilo...

3 months ago

Solved

Convert Hexavigesimal to Decimal
NASA (Ned’s Alien-Spying Agency) have made contact with a 13-fingered race from the planet Genai. Naturally, Ned’s shadowy opera...

3 months ago