<2008-02-02> by Lorenzo Bolla

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!