Problem #88 concerns numbers which can be expressed as both the sum and the product of the numbers in the same set of numbers. The question reads: Project Euler Problem 88: Product-sum numbers A natural number, N, that can be written as the sum and product of a given set of at least two natural …
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Project Euler Problem #87
Problem #87 concerns numbers which can be written as the sum of a perfect square, a perfect cube, and a perfect fourth power of prime numbers. The question reads: Project Euler Problem 87: Prime power triples The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is 28. …
Project Euler Problem #86
Problem #86 concerns the surface area diagonal of rectangular prisms. The question reads: My solution for this problem definitely falls into the category of brute force. Here is my solution: Solution #1: Brute Force Approach Let F(M) be the number of cuboids with this property ignoring rotations with dimensions less than or equal to M. …
Project Euler Problem #85
Problem #85 concerns finding the number of rectangles with sides along a lattice grid. The question reads: This problem is very well known among those who participate in math competitions. Here is my solution: Solution #1: Combinatorial Approach We can observe that in a grid with m horizontal lines and n vertical lines, any rectangle …
Project Euler Problem #84
Problem #84 concerns simulations of the game Monopoly. The question reads: I apologize for not embedding this problem in WordPress. I felt it would be much simpler if I just added a screenshot due to the long list of instructions. Regardless, this is one of the more intimidating early questions of Project Euler. My solution …
Project Euler Problem #83
Problem #83 is a more complex version of Problems #81 and #82. The question reads: Project Euler Problem 83: Path sum: four ways In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by moving left, right, up, and down, is indicated in bold red and …
Project Euler Problem #82
Problem #82 is a more complex version of Problem #81. The question reads: Project Euler Problem 82: Path sum: three ways The minimal path sum in the 5 by 5 matrix below, by starting in any cell in the left column and finishing in any cell in the right column, and only moving up, down, …
Project Euler Problem #81
Problem #81 concerns finding the minimum weighted path along the rows and columns of a grid. The question reads: Project Euler Problem 81: Path sum: two ways In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by only moving to the right and down, is indicated …
Project Euler Problem #80
Problem #80 concerns the digits of the decimal expansions of irrational square roots. The question reads: Project Euler Problem 80: Square root digital expansion It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such square roots is infinite without …
Project Euler Problem #79
Problem #79 concerns finding the shortest string with given substrings. The question reads: Project Euler Problem 79: Passcode derivation A common security method used for online banking is to ask the user for three random characters from a passcode. For example, if the passcode was 531278, they may ask for the 2nd, 3rd, and 5th …
The Inner Machinations of Walker 