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The Problem: Moving through a triangle of number (every number chosen yields 2 more numbers to choose), what is the highest sum path in the triangle? Considerations and Approach: We will populate a tree data structure with the data from the triangle, and th...

The Problem: How many Sundays fell on the first of the month between Jan 1 1901 and Dec 31 2000? Considerations: There is for sure a number theory mathematical way of handling this... but... Approach: What if we just imported a python calendar module and ...

The Problem: What is the sum of the digits of 100! where n! means 1x2x3x4x...xn? Considerations and Approach: For Python this is trivial to produce 100! and then take the sum of the digits by converting to a string and back. The Code: import math ...

The Problem: Let d(n) be defined as the sum of proper divisors of (numbers less than n which divide evenly into n).If d(a) = b and d(b) = a, where a =/= b, then a and b are an amicable pair and each of a and b are called amicable numbers. For example, the pr...

The Problem: Get the total sum of a file of names if each letter in the name is mapped from 1-26 and then multiplied by the position in an alphabetical sort. Considerations and Approach: We read in the file into an array of names. After that it just needs t...

The Problem: A perfect number is a number for which the sum of its proper divisors is exactly equal to the number.  A number is called deficient if the sum of its proper divisors is less than and it is called abundant if this sum exceeds. As 12 is the smalle...

The Problem: What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9? Considerations and Approach: Well, this is another problem that Python has a simple built in way... Generating all of the permutations of the number...

The Problem: What is the first Fibonacci number with 1000 digits? Considerations and Approach: This is somewhat trivial with Python since it can store a 1000 digit number with relative ease, and we don't need to run a super efficient Fibonacci algorithm or ...

The Problem: If you were to build a square starting with 1 in the middle then going right, down, left 2, up 2, right 2, and repeat, all the corner numbers would be diagonals. On the Project Euler website there is a nice graphic that I'm not putting here. Wh...

The Problem: Find the value of a,b of n^2 + an + b where |a| < 1000 and |b| <= 1000 where starting from n = 0 and incrementing, there is the largest consecutive chain of primes. Considerations and Approach: The way that we can approach this is by incrementi...

The Problem: How many distinct terms are in the sequence generated by a^b for a and b being bounded to 2 and 100 inclusive? Considerations and Approach: Naively, this is only processing 100*100 numbers, not really much at all.  We can create a python set an...

Hello, I'm Maxwell, and this is Mundane Meme, my weird blogging site. I mostly post solutions (that are honestly a little scuffed) to some of the Euler Problems, but I'm hoping to populate this website with more content... really just for my own enjoyment/po...

The Problem: Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits: 1634, 8208, 9474  We ignore 1 for the trivial case,lol. Find the sum of all the numbers that can be written as the sum of fifth powers of ...

The Problem: Pandigital numbers are numbers that have 1-n shown exactly once.  7254 is unusual because 39 * 186 = 7254, which is pandigital through the whole calculation.   What is the sum of all products that can generate these pandigital calculations? Consid...

The Problem: The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.  We shall consider fractions like, 30/50=3/5, to...

The Problem: Find the sum of all numbers equal to the sum of their factorials. Considerations and Approach: We can find the upper limit by filling a number with 9s and checking that the sum of the digits is greater than the factorial of the number. After we fi...