# Euler problems/71 to 80

## Contents

## Problem 71

Listing reduced proper fractions in ascending order of size.

Solution:

```
problem_71 = undefined
```

## Problem 72

How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000?

Solution:

```
problem_72 = undefined
```

## Problem 73

How many fractions lie between 1/3 and 1/2 in a sorted set of reduced proper fractions?

Solution:

```
problem_73 = undefined
```

## Problem 74

Determine the number of factorial chains that contain exactly sixty non-repeating terms.

Solution:

```
problem_74 = undefined
```

## Problem 75

Find the number of different lengths of wire can that can form a right angle triangle in only one way.

Solution:

```
problem_75 = undefined
```

## Problem 76

How many different ways can one hundred be written as a sum of at least two positive integers?

Solution:

```
problem_76 = undefined
```

## Problem 77

What is the first value which can be written as the sum of primes in over five thousand different ways?

Solution:

```
problem_77 = undefined
```

## Problem 78

Investigating the number of ways in which coins can be separated into piles.

Solution:

```
problem_78 = undefined
```

## Problem 79

By analysing a user's login attempts, can you determine the secret numeric passcode?

Solution:

```
problem_79 = undefined
```

## Problem 80

Calculating the digital sum of the decimal digits of irrational square roots.

Solution:

```
problem_80 = undefined
```