# Euler problems/31 to 40

## Contents

## Problem 31

Investigating combinations of English currency denominations.

Solution:

This is the naive doubly recursive solution. Speed would be greatly improved by use of memoization, dynamic programming, or the closed form.

```
problem_31 = pence 200 [1,2,5,10,20,50,100,200]
where pence 0 _ = 1
pence n [] = 0
pence n denominations@(d:ds)
| n < d = 0
| otherwise = pence (n - d) denominations
+ pence n ds
```

## Problem 32

Find the sum of all numbers that can be written as pandigital products.

Solution:

```
problem_32 = undefined
```

## Problem 33

Discover all the fractions with an unorthodox cancelling method.

Solution:

```
problem_33 = undefined
```

## Problem 34

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

Solution:

```
problem_34 = undefined
```

## Problem 35

How many circular primes are there below one million?

Solution:

```
problem_35 = undefined
```

## Problem 36

Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2.

Solution:

```
problem_36 = undefined
```

## Problem 37

Find the sum of all eleven primes that are both truncatable from left to right and right to left.

Solution:

```
problem_37 = undefined
```

## Problem 38

What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ?

Solution:

```
problem_38 = undefined
```

## Problem 39

If p is the perimeter of a right angle triangle, {a, b, c}, which value, for p ≤ 1000, has the most solutions?

Solution:

```
problem_39 = undefined
```

## Problem 40

Finding the nth digit of the fractional part of the irrational number.

Solution:

```
problem_40 = undefined
```