# Euler Solution 32

### From ProgSoc Wiki

The product 7254 is unusual, as the identity, 39 × 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.

# Solutions

## Python by Althalus

Runtime: 1.5 seconds

def isPan(a,b,c): list = [] for char in str(a): if char not in list: list.append(char) for char in str(b): if a not in list: list.append(char) for char in str(c): if char not in list: list.append(char) if len(list) == 9: for i in range(1,10): if str(i) not in list: return False return True return False list = [] total = 0 #sqrt(987654321) = 32426. By the time we pass this, we'll have covered everything. for a in range(1,10): for b in range(1,10000): c = a*b if panLength(a,b,c) == 9: if isPan(a,b,c): if c not in list: print a,b,c list.append(c) #if panLength(a,b,c) > 9: break for a in range(1,100): for b in range(1,1000): c = a*b if panLength(a,b,c) == 9: if isPan(a,b,c): if c not in list: #print c list.append(c) #if panLength(a,b,c) > 9: break for num in list: total =total+ num print total