permutations[prime_sorted_digits].append(prime)
else:
permutations[prime_sorted_digits] = [prime]
# Keep only those with at least three primes
permutations = {
sorted_digits: primes
for sorted_digits, primes in permutations.items() if len(primes) >= 3
}
# Get arithmetic sequences of length 3
progressives = []
for primes in permutations.values():
# Pick all prime triplets
for combo in combinations(primes, 3):
#Check for progression
if combo[2] - combo[1] == combo[1] - combo[0]:
progressives.append(combo)
#There should be two sequences
assert len(progressives) == 2
# Remove known sequence
progressives.remove((1487, 4817, 8147))
the_seq = progressives[0]
return ''.join(str(prime) for prime in the_seq)
if __name__ == '__main__':
start.time_functions(p49)
#dn_todo = [1,10]
dn_list = []
n = 0
num = 0
while len(dn_todo):
num += 1
pre_n = n
n += len(str(num)) #Can optimise this
while len(dn_todo) and pre_n <= dn_todo[0] and dn_todo[0] <= n:
n_wanted = dn_todo[0]
del dn_todo[0]
#We note:
#Current num is the number leading to the n boundary
#1234
# * ^
# n=102
dn_list.append(str(num)[-(n - n_wanted) - 1])
p = 1
for x in [int(s) for s in dn_list]:
p *= x
return p
if __name__ == "__main__":
import utility.start as start
start.time_functions(p40)
''' https://projecteuler.net/problem=41
Assuming n can be 9 maximum.
n cannot be 9 because sum of 1, ..., 9 is 45 and thus divisible by 9.
n cannot be 8 because sum of 1, ..., 8 is 36 and thus divisible by 9.
Thus I am assuming n is 7.
'''
from utility import start, primes2, generic
def p41():
MAX_NUM = 7654321
prime_list = primes2.PrimeList()
prime_list.sieve(MAX_NUM)
max_prime_pandigital = 0
for prime in prime_list.get_primes_in(generic.grange(MAX_NUM, -1)):
if ''.join(sorted(str(prime))) == '1234567':
max_prime_pandigital = prime
break
return max_prime_pandigital
if __name__ == '__main__':
start.time_functions(p41)
def concatenated_product(k, n):
single_products = [k * i for i in range(1, n + 1)]
return int(''.join([str(product) for product in single_products]))
def is_pandigital(number):
return sorted(str(number)) == ['1', '2', '3', '4', '5', '6', '7', '8', '9']
def p38():
# k = 1 cases:
largest_pandigital = concatenated_product(1, 9)
checks = [(5, 9, 5), (25, 33, 4), (100, 333, 3), (5000, 9999, 2)]
for check in checks:
k_start = check[0]
k_end = check[1]
n = check[2]
for k in range(k_start, k_end + 1):
possible = concatenated_product(k, n)
if possible > largest_pandigital and is_pandigital(possible):
largest_pandigital = possible
return largest_pandigital
if __name__ == '__main__':
start.time_functions(p38)
'''
import itertools
from utility import start
def p43():
def check_three(number, start, div_by):
return ((100 * number[start] + 10 * number[start + 1] +
number[start + 2]) % div_by == 0)
found = []
base = '0123456789'
for pd in itertools.permutations(base):
#Filler just so d_1 corresponds to 1st digit
pd = ['filler'] + [int(digit) for digit in pd]
if pd[4] in (0, 2, 4, 6, 8): #Could optimise ordering of ifs:
if sum(pd[3:6]) % 3 == 0:
if pd[6] in (0, 5):
if check_three(pd, 5, 7):
if check_three(pd, 6, 11):
if check_three(pd, 7, 13):
if check_three(pd, 8, 17):
found.append(pd[1:])
return sum(int(''.join(str(digit) for digit in snum)) for snum in found)
if __name__ == '__main__':
start.time_functions(p43)
odd = 2 + 2*square ==> prime != 2
1, 3, 5, 7 are not composite; Problem checked up to 33.
Work up from 35, 37... and subtract 2*square and see if any is prime.
square starts from 1, because odd must be a composite.
square inclusively ends at math.floor(math.sqrt((odd - 3) / 2))
'''
import math
from utility import start, generic, primes2
def p46():
primes = primes2.PrimeList()
for odd in generic.grange(35, 2):
if primes.is_prime(odd):
continue
for psquare in range(1, math.floor(math.sqrt((odd - 3) / 2)) + 1):
square = 2 * psquare**2
if primes.is_prime(odd - square):
break
else:
return odd
if __name__ == '__main__':
start.time_functions(p46)
"""
import fractions
from utility import start
def p33():
the_fracs = []
for denominator in range (11, 100):
c = denominator // 10
d = denominator % 10
if d == 0:
continue
for numerator in range(11, denominator):
a = numerator // 10
b = numerator % 10
if b == 0:
continue
frac = numerator/denominator
if (a == c and frac == b/d) or (a == d and frac == b/c) or\
(b==c and frac == a/d) or (b == d and frac == a/c):
the_fracs.append(fractions.Fraction(numerator, denominator))
final_frac = fractions.Fraction(1)
for frac in the_fracs:
final_frac *= frac
return final_frac.denominator
if __name__ == '__main__':
start.time_functions(p33)
new_prime = int(str_prime[i:])
if not pl.is_prime(new_prime):
break
else:
truncated_primes.append(new_prime)
else:
return truncated_primes
return None
def p37a():
real_answer = []
pg = pl.get_primes(10)
prime = 2
while prime < 10**6:
prime = next(pg)
truns = get_truncates(prime)
if truns:
real_answer.append(prime)
if len(real_answer) == 11:
break
return sum(real_answer)
if __name__ == '__main__':
import utility.start as start
start.time_functions(p37a)
max_l = current_l
return the_p
def p39b():
py_triples = {}
for p in range(12, 1001, 2):
max_a = m.ceil((p / 3) - 1)
for a in range(3, max_a + 1):
b = p * (2 * a - p) / (2 * (a - p)) #Must be whole number
#print(p, a, b, p-a-b)
if m.floor(b) == m.ceil(b):
#We have a triple
if p not in py_triples:
py_triples[p] = []
py_triples[p].append((a, b))
the_p = 0
max_l = 0
for perimeter, solns in py_triples.items():
current_l = len(solns)
if current_l > max_l:
the_p = perimeter
max_l = current_l
return the_p
if __name__ == '__main__':
import utility.start as start
start.time_functions(p39b)
from utility import start, integers
def get_working_size(n, r):
"""Return all k s.t. nCk > X, given smallest r such that nCr > X"""
return n - 2 * r + 1
def p53():
num_values = 0
# First ones that work from question
n = 23
r = 10
while n <= 100:
# We under-shoot the r value by 1:
while integers.choose(n, r) >= 10**6:
r -= 1
# The last r that worked is actually r + 1:
num_values += get_working_size(n, r + 1)
n += 1
return num_values
if __name__ == '__main__':
start.time_functions(p53)
break
cur_answer = maths.floor(numerator[current_num_i] / denom)
carry = numerator[current_num_i] % denom
try:
numerator[current_num_i+1] = carry * 10 +\
numerator[current_num_i+1]
except IndexError:
numerator.append(carry*10)
answer.append(cur_answer)
working_number_list.append(numerator[current_num_i])
#print(list(set(working_number_list)), working_number_list)
repeating_section_info.append((denom, len(repeat_section),
repeat_section))
#Analyse repeating_section_info
max_length = (0, 0, 0)
for denom, length, section in repeating_section_info:
print(denom, length, section)
if length > max_length[1]:
max_length = (denom, length, section)
return max_length[0]
if __name__ == '__main__':
import utility.start as start
start.time_functions(p26)
LOL (Micket):
"I think i few people missed the fact that 1*x didn't have to contain the same
numbers (althought it did happen to have)"
"""
def p52():
#ALL THESE IFs COULD HAVE BEEN REPLACED WITH A LOOP!!
for x in range(142857, 10000000):
x2 = 2 * x
if sorted(list(str(x))) == sorted(list(str(x2))):
#return x
x3 = 3 * x
if sorted(list(str(x))) == sorted(list(str(x3))):
#return x
x4 = 4 * x
if sorted(list(str(x))) == sorted(list(str(x4))):
#return x
x5 = 5 * x
if sorted(list(str(x))) == sorted(list(str(x5))):
#return x
x6 = 6 * x
if sorted(list(str(x))) == sorted(list(str(x6))):
return x
if __name__ == '__main__':
import utility.start as start
start.time_functions(p52)
import itertools
import utility.start as start
def p32():
valid_products = set()
for k in (1, 2):
base = '123456789'
for m1 in itertools.permutations(base, k):
remaining = base
for l in m1:
remaining = remaining.replace(l, '')
m1 = int(''.join(m1))
for m2 in itertools.permutations(remaining, 5-k):
remaining2 = remaining
for l in m2:
remaining2 = remaining2.replace(l, '')
m2 = int(''.join(m2))
p = m1 * m2
if sorted(str(p)) == list(remaining2):
valid_products.add(p)
return sum(valid_products)
if __name__ == '__main__':
start.time_functions(p32)
remaining_value = value - first_coin
if remaining_value < 0:
break
if remaining_value != 0:
new_max_denom = min(max_denom, remaining_value, first_coin)
for new_max_denom in [c for c in ctable if c <= new_max_denom]:
new_possibles = form(remaining_value, new_max_denom)
for new_possible in new_possibles:
addto = [first_coin]
addto.extend(new_possible)
addto.sort(reverse=True)
possibles.append(addto)
else:
possibles.append([first_coin])
possibles = remove_dups(possibles)
return possibles
def p31():
possibilities = form(200, 200)
#for p in possibilities:
# print(p)
print(form.cache_info())
return len(possibilities)
if __name__ == '__main__':
start.time_functions(p31)
t += 1
t_num = integers.get_triangle_number(t)
if t_num == p_num:
return (t_num, t, p37a, h)
elif t_num > p_num:
break
elif p_num > h_num:
break
for n, t_num in enumerate(integers.get_triangle_numbers()):
x = 166 #x=165 is the first one
p_num = get_pentagonal_number(x)
while p_num < t_num:
x += 1
p_num = get_pentagonal_number(x)
if p_num == t_num:
y = 144 #y=143 is the first one
h_num = get_hexagonal_number(y)
while h_num < t_num:
y += 1
h_num = get_hexagonal_number(y)
if h_num == t_num:
return (t_num, n + 1, x, y) #n starts from 0
if __name__ == '__main__':
start.time_functions(p45)
except IndexError:
consider_nexts.append((pair[0], pair[1]))
diffs_list.append(diff)
add_next_gen()
while True:
smallest_diff = min(diffs_list)
index_smallest = diffs_list.index(smallest_diff)
pair = consider_nexts[index_smallest]
# If smallest_diff is in last generator, add in next generator
if index_smallest == len(diffs_list) - 1:
add_next_gen()
update(index_smallest)
yield pair[0], pair[1], smallest_diff
def p44():
pentagonals = generic.Sliceable(integers.get_pentagonals(),
generic.Sliceable.less_than_last)
for p1, p2, sub_dif in get_smallest_diffs(pentagonals):
if sub_dif in pentagonals and p1 + p2 in pentagonals:
return sub_dif
if __name__ == '__main__':
start.time_functions(p44)
elif is_three_kind():
return (4, is_three_kind())
elif is_two_pairs():
return [3] + is_two_pairs()
def is_player1_winner(hand1, hand2):
'''Return if Player 1 wins (player 1 is hand1)'''
s1, s2 = (score_hand(hand1), score_hand(hand2))
for i in range(len(s1)):
if s1[i] > s2[i]:
return True
elif s1[i] < s2[i]:
return False
raise Exception("They are all equal!")
def p54():
player1_hands, player2_hands = parse_datafile()
player1_wins = [
is_player1_winner(player1_hands[i], player2_hands[i])
for i in range(len(player1_hands))
]
return player1_wins.count(True)
if __name__ == '__main__':
start.time_functions(p54)
"j": 10,
"k": 11,
"l": 12,
"m": 13,
"n": 14,
"o": 15,
"p": 16,
"q": 17,
"r": 18,
"s": 19,
"t": 20,
"u": 21,
"v": 22,
"w": 23,
"x": 24,
"y": 25,
"z": 26
}
value = sum(letter_values[char] for char in word.lower())
return value
word_sums = [letter_sum(word) for word in words]
num_triangles = sum(1 for word_sum in word_sums
if integers.is_triangle_number(word_sum))
return num_triangles
if __name__ == '__main__':
start.time_functions(p42)
''' https://projecteuler.net/problem=47
'''
import math
from utility import start, generic, primes2
def p47():
pass
if __name__ == '__main__':
start.time_functions(p47)