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Easy Sequences 33: Web Trapped Ant
An ant is trapped on a spider web inside a can with open top. The can has a radius and height . A spider sitting on the outside...

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Easy Sequences 30: Nearly Pythagorean Triangles
A Nearly Pythagorean Triangle (abbreviated as "NPT'), is an integer-sided triangle whose square of the longest side, which we wi...

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Easy Sequences 26: Prime-Integer Line Segments
At the first quadrant in the -plane, you are asked to construct a line segment with the following specifications: Select a prim...

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Easy Sequences 25: Product of Series
The function 'P(n)' is defined as the series product: where 'T(n)' is the triangular sum: ...

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Easy Sequences 28: Sum of Radicals of Integers
The radical of a positive integer is defined as the product of the distinct prime numbers dividing . For example, the distinct ...

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Easy Sequences 27: Product of Radicals of Integers
The radical of a positive integer is defined as the product of the distinct prime numbers dividing . For example, the distinct ...

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Easy Sequences 31: N-N's Sequence
We define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number ...

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Easy Sequences 24: Number of Coprime Lattice Points
Given a number 'n', you were tasked to mark and count all coprime lattice points at the first quadrant bounded by the points (0,...

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Easy Sequences 23: Hat Guessing Game!
Consider the following Game Show: Hats, with numbers written on each, were placed on the heads of the participants. Participant...

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Easy Sequences 21: Combinatorial Summations
Create the function S(n), defined by the following summation: The symbol is the combination f...

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Easy Sequences 18: Set Bits of Triple Summations
The function S(n) is defined by the following triple summations: The double brackets mean that th...

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Easy Sequences 16: Volume of Embedded Octahedron
An octahedron (not regular) is formed by joining the centers of the faces of a rectangular parallelepiped (see below figure). ...

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Easy Sequences 13: Average Speed of Spaceship
A certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ...

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Rotating the plane region bounded by two polynomials
Let p and q be n-degree and m-degree polynomials with n >= m >= 1. Consider clockwise rotate the plane region bounded by these t...

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Comparing to scale all terms versus one term of even-degree polynomial by the same scale factor
Let p be an even-degree polynomial with positive leading coefficient. Consider the scale factor, k, that vertically transforms ...

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Breaking straight lines
Let P be a point in Oxy plane and let p be a 1×2 array representing an one-degree or zero-degree polynomials, if its first entry...

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Rotating 2d curve around a vertical axis
Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotatio...

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Scaling vertically parabola by evaluating its area over an interval
Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the...

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Scaling vertically functions
Given a real function by the 1×n array, x, of inputs and the 1×n array, y, of outputs, consider shifting vertically its graph by...

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Shifting vertically a function's graph
Given a real function, f, by n input-output pairs, consider a translation in the up-down direction given by an amount k. For a ...

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Shifting vertically even-degree polynomial's graph by its mean over an interval
Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by...

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Translating even-degree polynomial by its vertex to the origin
Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting ...

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Translating parabola by its vertex to the origin
Given a quadratic polynomial, p(x) = ax^2 + bx + c (a ~= 0), represented by the vector [a b c], consider the translation of the ...

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Slicing a 4-pointed star polygon
Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h ...

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Covering a 4-pointed star polygon by a circle sector
Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h ...

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Covering a four-pointed star polygon by circles
Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their...

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Slicing the area of a circle
Given the area, A, of a square, consider a circle having the area, πA, and the radius, r. For a given slicing number n>1, find ...

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Covering a four-pointed star polygon by rectangles
Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their...

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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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