# IQ test

Qualche giorno fa, mi sono imbattuto in questo test di intelligenza, proposto da ECM. Riporto il testo, per semplicita':

Using each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 only once, form a nine digit number A that can satisfy the following criteria:

- A is exactly divisible by 9.
- Removing the rightmost digit from A forms an eight digit number B that is exactly divisible by 8.
- Removing the rightmost digit from B forms a seven digit number C that is exactly divisible by 7.
- Removing the rightmost digit from C forms a six digit number D that is exactly divisible by 6.
- Removing the rightmost digit from D forms a five digit number E that is exactly divisible by 5.
- Removing the rightmost digit from E forms a four digit number F that is exactly divisible by 4.
- Removing the rightmost digit from F forms a three digit number G that is exactly divisible by 3.
- Removing the rightmost digit from G forms a two digit number H that is exactly divisible by 2.
What is A?

Show how you produced B, C, D, E, F, G & H.

Dopo un po', mi sono stufato, e ho prodotto questo.

def all_perms(str): if len(str) <=1: yield str else: for perm in all_perms(str[1:]): for i in range(len(perm)+1): yield perm[:i] + str[0:1] + perm[i:] def list2num(p): y = 0 d = len(p) for ip,pp in enumerate(p): y += 10**(d-ip-1) * pp return y def check(p): for i in xrange(1,len(p)-1): if list2num(p[:-i]) % (9-i) != 0: return False return True for p in all_perms(range(1,10)): if check(p): print p break

Run it in python, of course!