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Does the coin touch the line?
If we throw a coin that has a diameter of d, its center will land in a grid n x m. What is the probability that the coin land...

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Convert a diagonal representation of a matrix element to linear index or subscripts
Elements in matrices in MATLAB can be retrieved by linear index or subscripts. For example, the 1 in the matrix below has a line...

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Determine whether a number is a repfigit number
A sequence of numbers is constructed from a number with the following steps: List the digits of . Compute the ()st term as t...

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Extract numbers using a decaying sieve
The Sieve of Eratosthenes is one method of determining primes. Starting with 2, one keeps 2 and removes 2x2, 3x2, 4x2, etc. Then...

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Find the Nth number in the 7-sequence
Find the Nth number in the 7-sequence. 7, 14, 21, 28, 35, 42, 49, 56, 63, 77, 84, ... Hint: Refer test suites

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

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FEN Chess Notation
Given an 8-by-8 character matrix representing a chess board, convert it to FEN (Forsyth-Edwards Notation) board position format....

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Can I make a right triangle ?
Input(a) - is vector with any amount of values. Interpreted as legths of sides. Output(b): * Is true if there are any 3 va...

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Apply the planing transform to natural numbers
Claude Lenormand’s planing (or raboter, in French) transform removes one element from each run in a sequence; that is, imagine a...

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Half-Swap
Given a vector with an even number of elements, rearrange it so that the elements in its first half are switched with those i...

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Return the Square of a Number
Write a function that takes a single numeric input x and returns its square. That is, given x, your function should output x^2....

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Find the smallest prime with n inside
Consider the sequence that begins 101, 113, 127, 131, 149, 151, 163,... Not only is every term prime, the th term is the smalles...

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Express base-10 integers in lazy binary
The binary (or base-2) representations of a number n can be constructed as follows: Step 1: If n = 0, then the binary represent...

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Find Solutions to Edge-Matching Puzzles
I was intrigued by some edge-matching puzzles I came across when visiting my parents over Thanksgiving. "An edge-matching puzzle...

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How tall will my cactus be?
My Barbed Wire Cactus is a desert cactus that relies on just the right amount of rainfall to stay healthy. Given a 1×12 vector...

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Slicing the area of a regular polygon
Given the area, A, of a regular polygon with n sides, each of length s, consider its decomposition in congruent isosceles triang...

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Covering rectangle area of a four-pointed star polygon
Given the four-pointed star polygon formed by the rectangle, with dimensions l1xl2, and four triangles, with height, h, from the...

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Height of a four-pointed star polygon
Given the area A, of a rectangle with dimensions l1xl2, where the side lengths are integers and form the smallest possible perim...

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

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Compute MOSFET oxide thickness
Calculate the oxide thickness in nanometers for an NMOS on a p-type substrate. Inputs (all scalars): NA — acceptor concentrat...

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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...

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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...

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Square area to triangle area
Given the area, A, of a square with side length, c, if a right angle triangle has the same area A and the hypothenuse length 2c ...

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Radioactive Decay Chain
A radioactive decay chain consists of a series of nuclides, each decaying into the next. Suppose we have a chain of N isotopes:...

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Enclosure Matrix
The problem gives you a positive integer n. You need to create a matrix consisting of n layers of natural numbers; the outermost...

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Barnes G-Function
Evaluate the Barnes G-Function at a given (integral) value. %Example 1 in = 1; out = 1; %Example 1 in = 4; out = 2; ...

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Compute the Dedekind psi function
Write a function to compute the Dedekind psi function. The values for n = 1, 2, 3, 4, 5, and 6 are 1, 3, 4, 6, 6, and 12.

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Sum of series III
What is the sum of the following sequence: Σ(2k-1)^3 for k=1...n for different n?

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Sum of series II
What is the sum of the following sequence: Σ(2k-1)^2 for k=1...n for different n?

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Sum of series I
What is the sum of the following sequence: Σ(2k-1) for k=1...n for different n?

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