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Count the ways to write 1/n as the sum of two unit fractions
The number 1/2 can be written as 1/3+1/6 and 1/4+1/4, and the number 1/9 can be written as 1/18+1/18, 1/12+1/36, and 1/10+1/90. ...

3 months ago

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Classify numbers as abundant, deficient, or perfect
A number is perfect if the sum of its proper divisors (i.e., divisors excluding the number itself) is equal to itself. For examp...

3 months ago

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Calculating the Union Area of Overlapping Rectangles
Calculate the area covered by a union of multiple rectangles. Each rectangle is represented by 4 integers: the first two integer...

3 months ago

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List primes of the form xy+z
Consider three consecutive integers , , and . When is the number prime? For example, if or , then the results are 17 and 37, ...

3 months ago

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Extend the digamma function to negative arguments
While solving one of Ramon Villamangca’s problems, I needed the value of , where is the digamma function. However, MATLAB’s fun...

3 months ago

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Identify winnable games of Take a Square
A game has a pile of tokens, and two players alternate in taking a certain number of tokens from the pile, with the constraint t...

3 months ago

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Conditional transpose
You're given two vectors of the same length, x and y, which might be row or a column vectors. Your task is to ensure that y has ...

3 months ago

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Find the closest geyser prime
My wife and I celebrated our honeymoon and our recent anniversary in Yellowstone and Grand Teton National Parks. After returning...

3 months ago

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Delete some elements in the natural set and find the sum of the first n terms
Delete the number (except 0，1) with a complete square number from the natural set of numbers, form a new set of numbers, find th...

3 months ago

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List the partitions of an integer
Several Cody problems deal with partitions of an integer, or the ways an integer can be written as the sum of positive numbers—...

3 months ago

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Find the Nth number in the 8-sequence
Find the Nth number in the 8-sequence. 8, 16, 24, 32, 48, 56, 64, 72, 88, ... Hint: Refer test suites

3 months ago

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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

3 months ago

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Find the Nth number in the 6-sequence
Find the Nth number in the 6-sequence. 6, 12, 18, 24, 36, 42, 48, 54, 66, ... Hint: Refer test suites

3 months ago

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Find the Nth number in the 5-sequence
Find the Nth number in the 5-sequence. 5, 15, 25, 35, 45, 55, ... Hint: Refer test suites

3 months ago

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Find the Nth number in the 4-sequence
Find the Nth number in the 4-sequence. 4, 8, 12, 16, 24, 28, 32, 36, 44 ... Hint: Refer test suites

3 months ago

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Find the Nth number in the 3-sequence
Find the Nth number in the 3-sequence. 3, 6, 9, 12, 15, 18, 21, 24, 27, 33 ... Hint: Refer test suites

3 months ago

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Find the Nth number in the 2-sequence.
Find the Nth number in the sequence. 2, 4, 6, 8, 12, 14, 16, 18, 22, ... Hint: Refer test suites

3 months ago

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2x2 binning of a large sparse matrix
Consider the 20000 x 20000 sparse matrix, A=round(sprand(2e4,2e4,1/1e4*100)*1000); The task is to divide this matrix into 2x...

3 months ago

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Build a block Toeplitz matrix
A symmetric block Toeplitz matrix has the form, where the are compatibly-sized matrices. Write a routi...

3 months ago

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Identify points inside a Reuleaux triangle
Write a function to identify points that lie in or on a Realeaux triangle, which is a curve of constant width. The input to the ...

3 months ago

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Express integers in negabinary
Negabinary numbers are written in base -2. For example, the negabinary number 11010 is , or 6 in base 10. In a similar way, -3 i...

3 months ago

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Count the primes resulting from changing one digit of a number
If you start with the number 24 and seek primes by changing a single digit, you can find two: 23 and 29. If you start with 130, ...

3 months ago

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Sum of Even Fibonacci Numbers
Description: The Fibonacci sequence is defined as follows:F(1)=1,F(2)=1,F(n)=F(n−1)+F(n−2) for n>2 Write a function that compu...

3 months ago

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Remove Duplicate Words from a Sentence
Given a sentence as a string, remove all duplicate words while keeping their first occurrence and maintaining the original word ...

3 months ago

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Remove Duplicate Words from a Sentence.
Given a sentence, remove any duplicate words, leaving only the first occurrence of each word. The output sentence should have wo...

3 months ago

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Project Euler Problem 48: Self Powers
The series,. Return a string of the last ten digits of the series:. Hint: Use modular arithmetic! Spoiler: The solution is...

3 months ago

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Check if a Number is a Palindrome Without Converting to String
Write a function that checks if a given positive integer is a palindrome without converting the number to a string or using stri...

3 months ago

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Greater than before
Given an array of integers, write a function that returns elements that are greater than the one before them. For instance, ...

3 months ago

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Symmetric Pair
Given an (n, 2) matrix, remove any symmetric pairs from the matrix. Keep the first occurrence. (2, 3) and (3, 2) are considere...

3 months ago

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Most Frequent Characters
Given a document file or a character array, identify the 'n' most frequently occurring characters and the number of times each a...

3 months ago