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 …
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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 …
Project Euler Problem #78
Problem #78 is yet another problem which involves partitions. The question reads: Project Euler Problem 78: Coin partitions Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can be separated into piles in exactly seven different ways, so p(5)=7. OOOOO OOOO O OOO OO OOO …
Project Euler Problem #77
Problem #77 concerns partitions of numbers where the summands in each partition are composed of the prime numbers less than the number. The question reads: Project Euler Problem 77: Prime summations It is possible to write ten as the sum of primes in exactly five different ways: 7 + 3 5 + 5 5 + …
Project Euler Problem #76
Problem #76 concerns partitions of positive integers. The question reads: Project Euler Problem 76: Counting summations It is possible to write five as a sum in exactly six different ways: 4 + 1 3 + 2 3 + 1 + 1 2 + 2 + 1 2 + 1 + 1 + 1 1 + …
Project Euler Problem #75
Problem #75 concerns the perimeters of right triangles with integer side lengths. The problem reads: Project Euler Problem 75: Singular integer right triangles It turns out that 12 cm is the smallest length of wire that can be bent to form an integer sided right angle triangle in exactly one way, but there are many …
Project Euler Problem #74
Problem #74 concerns the sum of the factorials of the digits in a number. The question reads: Project Euler Problem 74: Digit factorial chains The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145: 1! + 4! + 5! = 1 + 24 …
The Inner Machinations of Walker 