def p011(N=4):
besth = max(
numty.prod(grid[i][j + k] for k in range(N)) for i in range(len(grid))
for j in range(len(grid[0]) - N))
bestv = max(
numty.prod(grid[i + k][j] for k in range(N))
for i in range(len(grid) - N) for j in range(len(grid[0])))
bestd = max(
numty.prod(grid[i + k][j + k] for k in range(N))
for i in range(len(grid) - N) for j in range(len(grid[0]) - N))
bestu = max(
numty.prod(grid[i - k][j + k] for k in range(N))
for i in range(N, len(grid)) for j in range(len(grid[0]) - N))
return max(besth, bestv, bestd, bestu)
def p011(N=4):
besth = max(numty.prod(grid[i][j+k] for k in range(N))
for i in range(len(grid))
for j in range(len(grid[0])-N))
bestv = max(numty.prod(grid[i+k][j] for k in range(N))
for i in range(len(grid)-N)
for j in range(len(grid[0])))
bestd = max(numty.prod(grid[i+k][j+k] for k in range(N))
for i in range(len(grid)-N)
for j in range(len(grid[0])-N))
bestu = max(numty.prod(grid[i-k][j+k] for k in range(N))
for i in range(N,len(grid))
for j in range(len(grid[0])-N))
return max(besth, bestv, bestd, bestu)
def nthperm(N, l):
if len(l) == 1:
return l
lminus1fact = numty.prod(range(1, len(l)))
firstelt = N / lminus1fact
return [l[firstelt]] + nthperm(N % lminus1fact,
l[:firstelt] + l[firstelt + 1:])
def p033():
acc = set([])
for a in range(1, 10):
for b in range(1, 10):
for c in range(1, 10):
ab = 10 * a + b
ac = 10 * a + c
ca = 10 * c + a
bc = 10 * b + c
cb = 10 * c + b
acc.add(check(ab, ac, b, c))
acc.add(check(ab, ca, b, c))
acc.add(check(ab, bc, a, c))
acc.add(check(ab, cb, a, c))
product = numty.prod(acc)
return product.denominator
def p033():
acc = set([])
for a in range(1,10):
for b in range(1, 10):
for c in range(1, 10):
ab = 10*a+b
ac = 10*a+c
ca = 10*c+a
bc = 10*b+c
cb = 10*c+b
acc.add(check(ab, ac, b, c))
acc.add(check(ab, ca, b, c))
acc.add(check(ab, bc, a, c))
acc.add(check(ab, cb, a, c))
product = numty.prod(acc)
return product.denominator
def p040():
return numty.prod(d(10**k) for k in range(0,7))
#
# How to bound this?
# We don't need to check over 2! + 5*8! if only using digits 1..8.
# 9 is tricky because it's so big.
# The answer will need to be at least 6 digits long.
# If there is only one 9, we only need to check between 9! and 9!+5*8!
# If there are two 9s, 2*9! to 2*9!+4*8!
# A couple million things to check?
import logging
import lib.numty as numty
logger = logging.getLogger(__name__)
fact = [numty.prod(range(1,n+1)) for n in range(10)]
def p034():
acc = 0
ranges = [(10, fact[2] + 5 * fact[8])]
for n in range(1,7):
lower = n*fact[9]
upper = lower + fact[8]*(len(str(lower))-n)
ranges.append((lower, upper))
for l, u in ranges:
for n in range(l, u):
if sum(fact[int(d)] for d in str(n)) == n:
acc += n
logger.debug(n)
n += 1
return acc
def p020(N=100):
return sum(int(d) for d in str(numty.prod(range(1,N+1))))
def choose(n,k):
return int(numty.prod(Fraction(n-i,k-i) for i in range(k)))
def magic(n):
return sum(numty.prod(range(1,int(d)+1)) for d in str(n))
def phi(n, factoredn=None):
if not factoredn:
factoredn = numty.factor(n)
return numty.prod(p**(e-1)*(p-1) for p,e in factoredn.items())
def p040():
return numty.prod(d(10 ** k) for k in range(0, 7))
def radtable(n):
return [numty.prod(r.keys()) for r in utils.factortable(n)]
def nthperm(N, l):
if len(l) == 1:
return l
lminus1fact = numty.prod(range(1,len(l)))
firstelt = N/lminus1fact
return [l[firstelt]] + nthperm(N % lminus1fact, l[:firstelt]+l[firstelt+1:])
def rad(n):
return numty.prod(utils.factor(n).keys())
def p008(N=13):
return max(
numty.prod(int(d) for d in number[i:i + N])
for i in range(len(number) - N))
#
# How to bound this?
# We don't need to check over 2! + 5*8! if only using digits 1..8.
# 9 is tricky because it's so big.
# The answer will need to be at least 6 digits long.
# If there is only one 9, we only need to check between 9! and 9!+5*8!
# If there are two 9s, 2*9! to 2*9!+4*8!
# A couple million things to check?
import logging
import lib.numty as numty
logger = logging.getLogger(__name__)
fact = [numty.prod(range(1, n + 1)) for n in range(10)]
def p034():
acc = 0
ranges = [(10, fact[2] + 5 * fact[8])]
for n in range(1, 7):
lower = n * fact[9]
upper = lower + fact[8] * (len(str(lower)) - n)
ranges.append((lower, upper))
for l, u in ranges:
for n in range(l, u):
if sum(fact[int(d)] for d in str(n)) == n:
acc += n
logger.debug(n)
n += 1
def phi(n, factoredn=None):
if not factoredn:
factoredn = numty.factor(n)
return numty.prod(p**(e - 1) * (p - 1) for p, e in factoredn.items())
def p020(N=100):
return sum(int(d) for d in str(numty.prod(range(1, N + 1))))
def numdivs(factorization):
return numty.prod((e+1) for e in factorization.values())
def radtable(n):
return [numty.prod(r.keys()) for r in utils.factortable(n)]
def p008(N=13):
return max(numty.prod(int(d) for d in number[i:i+N])
for i in range(len(number)-N))
def numdivs(factorization):
return numty.prod((e + 1) for e in factorization.values())
def rad(n):
return numty.prod(utils.factor(n).keys())
