Project Euler: a Python (beginner friendly) approach to complex mathematical challenges

Sunday. January 17, 2021 - 9 mins

Leonhard Euler (1707-1783) was, without any doubt, one of the greatest mathematicians of all time. He is absolutely the most prolific, writing over 900 publications of work in different science fields (number theory, graph theory, analysis, physics, astronomy…). Matter of fact, an active effort was made to avoid naming everything after Euler and several theorems are attributed to the first person to have proved them after him.

Knowing this, it’s no surprise that Euler has become an idol and a role model to any aspiring mathematician (or engineer, or physicist, or…). The Project Euler is one of many tributes that has been made dedicated to Euler, inicially created as a subsection of our colleages in mathschallenge (a brilliant website to learn and enjoy mathematics). The Project Euler is a combination of mathematical problems that exists to encourage, challenge, and develop the skills and enjoyment of anyone with an interest in the fascinating world of mathematics.

In this page you will find my personal solutions to the problems, using only Python. They have been part of my process trying to learn Python and so, code can be messy or not optimized (sorry in advance). Every solution comes with small explanations, so it can serve as a Python learning experience, just as it was for me. Also, problems relying on tricky or advanced mathematics have a brief theorical explanation too.

I strongly encourage you to try and solve the problems without looking at any solution. Even if at first sight a problem feels overwhelming, give it a try and come back a few days later. You will be surprised at all the things you are capable of doing and you will learn even more.

And just remember, if everything goes wrong, here you’ll find some help. :)

This project is still a work in progress. Make sure to come back frecuently for the lastest updates!

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ID	Description / Title	Python Solution
1	Multiples of 3 and 5	Euler_001
2	Even Fibonacci numbers	Euler_002
3	Largest prime factor	Euler_003
4	Largest palindrome product	Euler_004
5	Smallest multiple	Euler_005
6	Sum square difference	Euler_006
7	10001st prime	Euler_007
8	Largest product in a series	Euler_008
9	Special Pythagorean triplet	Euler_009
10	Summation of primes	Euler_010
11	Largest product in a grid	Euler_011
12	Highly divisible triangular number	Euler_012
13	Large sum	Euler_013
14	Longest Collatz sequence	Euler_014
15	Lattice paths	Euler_015
16	Power digit sum	Euler_016
17	Number letter counts	Euler_017
18	Maximum path sum I
19	Counting Sundays
20	Factorial digit sum
21	Amicable numbers
22	Names scores
23	Non-abundant sums
24	Lexicographic permutations
25	1000-digit Fibonacci number
26	Reciprocal cycles
27	Quadratic primes
28	Number spiral diagonals
29	Distinct powers
30	Digit fifth powers
31	Coin sums
32	Pandigital products
33	Digit cancelling fractions
34	Digit factorials
35	Circular primes
36	Double-base palindromes
37	Truncatable primes
38	Pandigital multiples
39	Integer right triangles
40	Champernowne’s constant
41	Pandigital prime
42	Coded triangle numbers
43	Sub-string divisibility
44	Pentagon numbers
45	Triangular, pentagonal, and hexagonal
46	Goldbach’s other conjecture
47	Distinct primes factors
48	Self powers
49	Prime permutations
50	Consecutive prime sum
51	Prime digit replacements
52	Permuted multiples
53	Combinatoric selections
54	Poker hands
55	Lychrel numbers
56	Powerful digit sum
57	Square root convergents
58	Spiral primes
59	XOR decryption
60	Prime pair sets
61	Cyclical figurate numbers
62	Cubic permutations
63	Powerful digit counts
64	Odd period square roots
65	Convergents of e
66	Diophantine equation
67	Maximum path sum II
68	Magic 5-gon ring
69	Totient maximum
70	Totient permutation
71	Ordered fractions
72	Counting fractions
73	Counting fractions in a range
74	Digit factorial chains
75	Singular integer right triangles
76	Counting summations
77	Prime summations
78	Coin partitions
79	Passcode derivation
80	Square root digital expansion
81	Path sum: two ways
82	Path sum: three ways
83	Path sum: four ways
84	Monopoly odds
85	Counting rectangles
86	Cuboid route
87	Prime power triples
88	Product-sum numbers
89	Roman numerals
90	Cube digit pairs
91	Right triangles with integer coordinates
92	Square digit chains
93	Arithmetic expressions
94	Almost equilateral triangles
95	Amicable chains
96	Su Doku
97	Large non-Mersenne prime
98	Anagramic squares
99	Largest exponential
100	Arranged probability

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Thank you for your time and attention. Feel free to reach out if you have any questions or inquiries. I’d love to hear from you!

David Boo

Where biology, informatics & statistics intersect

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