def main(argv):
rna = fasta.read_one(argv[0])
au_max = max(rna.count('A'), rna.count('U'))
au_min = min(rna.count('A'), rna.count('U'))
cg_max = max(rna.count('C'), rna.count('G'))
cg_min = min(rna.count('C'), rna.count('G'))
print combinatorics.permutations(
au_max, au_min) * combinatorics.permutations(cg_max, cg_min)
def euler_41():
"What is the largest n-digit pandigital prime that exists?"
from combinatorics import permutations
# Pan-digital primes are 4 or 7 digits. Others divisible by 3
prime._refresh(2766) # sqrt(7654321)
x = list(range(7, 0, -1))
for perm in permutations(x):
num = 0
for n in perm:
num = num * 10 + n
if prime._isprime(num):
print("Lösung:", num)
break
def euler_43():
"Find the sum of all pandigital numbers with an unusual sub-string divisibility property."
from combinatorics import permutations
def num(l):
s = 0
for n in l:
s = s * 10 + n
return s
def subdiv(l, n):
return not num(l) % n
total = 0
for perm in permutations((0,1,2,3,4,6,7,8,9)):
perm.insert(5, 5) # d6 must be 5
if (subdiv(perm[7:10], 17) and
subdiv(perm[6:9], 13) and
subdiv(perm[5:8], 11) and
subdiv(perm[4:7], 7) and
subdiv(perm[3:6], 5) and
subdiv(perm[2:5], 3) and
subdiv(perm[1:4], 2)):
total += num(perm)
print("Lösung:", total)
def euler_49():
"Find arithmetic sequences, made of prime terms, whose four digits are permutations of each other."
from combinatorics import permutations
prime._refresh(10000)
for num in range(1000, 10000):
if str(num).find('0') >= 0:
continue
if prime.isprime(num):
prime_permutations = { num: 1 }
for x in permutations(list(str(num))):
next_num = int(''.join(x))
if prime.isprime(next_num):
prime_permutations[next_num] = 1
primes = sorted(prime_permutations.keys())
for a in range(0, len(primes)):
if primes[a] == 1487:
continue
for b in range(a+1, len(primes)):
c = (primes[a] + primes[b]) // 2
if c in prime_permutations:
print("Lösung:", str(primes[a]) + str(c) + str(primes[b]))
return
'''
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, 2143 is a 4-digit pandigital and is also prime.
What is the largest n-digit pandigital prime that exists?
'''
import prime
from combinatorics import permutations
# Pan-digital primes are 4 or 7 digits. Others divisible by 3
prime._refresh(2766) # sqrt(7654321)
for perm in permutations(range(7, 0, -1)):
num = 0
for n in perm: num = num * 10 + n
if prime._isprime(num):
print num
break
from combinatorics import permutations
def num(l):
s = 0
for n in l: s = s * 10 + n
return s
product = {}
for perm in permutations(range(1,10)):
for cross in range(1,4):
for eq in range(cross+1, 6):
a = num(perm[0:cross])
b = num(perm[cross:eq])
c = num(perm[eq:9])
if a * b == c: product[c] = 1
print sum(p for p in product)
d5 d6 d7 = 357 is divisible by 7
d6 d7 d8 = 572 is divisible by 11
d7 d8 d9 = 728 is divisible by 13
d8 d9 d10= 289 is divisible by 17
Find the sum of all 0 to 9 pandigital numbers with this property.
'''
from combinatorics import permutations
def num(l):
s = 0
for n in l: s = s * 10 + n
return s
def subdiv(l, n): return num(l) % n == 0
total = 0
for perm in permutations((0,1,2,3,4,6,7,8,9)):
perm.insert(5, 5) # d6 must be 5
if (subdiv(perm[7:10], 17) and
subdiv(perm[6:9], 13) and
subdiv(perm[5:8], 11) and
subdiv(perm[4:7], 7) and
subdiv(perm[3:6], 5) and
subdiv(perm[2:5], 3) and
subdiv(perm[1:4], 2)):
total += num(perm)
print total
def test_permutations_of_n_options():
assert permutations(10) == 3628800
def test_permutations_of_non_numeric_throws_exception():
with pytest.raises(Exception):
permutations([])
The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
What 12-digit number do you form by concatenating the three terms in this sequence?
'''
import prime
from combinatorics import permutations
prime._refresh(10000)
for num in xrange(1000, 10000):
if str(num).find('0') >= 0: continue
if prime.isprime(num):
prime_permutations = { num: 1 }
for x in permutations(list(str(num))):
next_num = int(''.join(x))
if prime.isprime(next_num):
prime_permutations[next_num] = 1
primes = sorted(prime_permutations.keys())
for a in xrange(0, len(primes)):
if primes[a] == 1487: continue
for b in xrange(a+1, len(primes)):
c = (primes[a] + primes[b]) / 2
if prime_permutations.has_key(c):
print str(primes[a]) + str(c) + str(primes[b])
exit()