The task in Problem 32 of Project Euler is:

We shall say that an $n$-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital. The product 7254 is unusual, as the identity, $39 \cdot 186 = 7254$, containing multiplicand, multiplier, and product is 1 through 9 pandigital. Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital. HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.

## How to solve it

We have to get a check, if a number is pandigital. It could look like this:

```
def isPandigitalString(string):
""" Check if string contains a pandigital number. """
digits = len(string)
if digits >= 10:
return False
for i in range(1, digits + 1):
if str(i) not in string:
return False
return True
```

We also need a check if a product of two numbers is 9-pandigital:

```
def gives9PandigitalProduct(a, b):
numbers = str(a) + str(b) + str(a * b)
if len(numbers) != 9:
return False
return isPandigitalString(numbers)
```

Now you need to figure out how to go through all possible combinations:

```
products = []
for a in range(0, 100000):
for b in range(a, 100000):
if len(str(a * b) + str(a) + str(b)) > 9:
break
if gives9PandigitalProduct(a, b):
products.append(a * b)
print("%i x %i = %i" % (a, b, a * b))
print(sum(set(products)))
```

## One-liner

This is from Thaddeus Abiye from Ethiopia:

```
print(
sum(
set(
map(
lambda x: int(x[0:4]),
filter(
lambda x: sorted([i for i in x]) == map(str, range(1, 10)),
[
str(a * b) + str(a) + str(b)
for a in range(1, 2000)
for b in range(1, 100)
],
),
)
)
)
)
```

It needs one line (if it was not black-formatted) and 173 characters, but I think it's hard to read.

## Data about my solution

- It worked in less than a second.
- 28 LOC (including whitespaces and comments)
- 719 characters for this solution (including whitespace and comments)