Project Euler — Problem 31 Solution

Problem

In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:

1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).

Project Euler — Problem 78 Solution

Problem

Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can separated into piles in exactly seven different ways, so p(5)=7.

Project Euler — Problem 76 Solution

Problem

It is possible to write five as a sum in exactly six different ways:

4 + 1

3 + 2

3 + 1 + 1

2 + 2 + 1

Project Euler — Problem 66 Solution

Problem

Consider quadratic Diophantine equations of the form:

x2 — Dy2 = 1

For example, when D=13, the minimal solution in x is 6492–13x1802 = 1.

Project Euler — Problem 77 Solution

Problem

It is possible to write ten as the sum of primes in exactly five different ways:

7 + 3

5 + 5

5 + 3 + 2

3 + 3 + 2 + 2

Project Euler — Problem 112 Solution

Problem

Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.

Similarly if no digit is exceeded by the digit to its right it is…

Project Euler — Problem 63 Solution

Problem

The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number, 134217728=89, is a ninth power.

How many n-digit positive integers exist which are also an nth power?

Project Euler — Problem 54 Solution

Problem

In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way:

• High Card: Highest value card.
• One Pair: Two cards of the…