# Euler problems/41 to 50

## Contents

## Problem 41

What is the largest n-digit pandigital prime that exists?

Solution:

```
problem_41 = undefined
```

## Problem 42

How many triangle words can you make using the list of common English words?

Solution:

```
problem_42 = undefined
```

## Problem 43

Find the sum of all pandigital numbers with an unusual sub-string divisibility property.

Solution:

```
problem_43 = undefined
```

## Problem 44

Find the smallest pair of pentagonal numbers whose sum and difference is pentagonal.

Solution:

```
problem_44 = undefined
```

## Problem 45

After 40755, what is the next triangle number that is also pentagonal and hexagonal?

Solution:

```
problem_45 = undefined
```

## Problem 46

What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?

Solution:

```
problem_46 = undefined
```

## Problem 47

Find the first four consecutive integers to have four distinct primes factors.

Solution:

```
problem_47 = undefined
```

## Problem 48

Find the last ten digits of 11 + 22 + ... + 10001000.

Solution:

```
problem_48 = undefined
```

## Problem 49

Find arithmetic sequences, made of prime terms, whose four digits are permutations of each other.

Solution:

```
problem_49 = undefined
```

## Problem 50

Which prime, below one-million, can be written as the sum of the most consecutive primes?

Solution:

```
problem_50 = undefined
```