from itertools import product

alphabet = '1234'

ap=[]

for i in product(alphabet, repeat=5):

if i.count('1') == 2:

ap.append(i)

print(len(ap))

from itertools import product

alphabet = '0123'

ap=[]

for i in product(alphabet, repeat=3):

if (i[0] != '0') and (int(i[0]) + int(i[2]) > int(i[1])):

ap.append(i)

print(len(ap))

count = 0

for i in '123':

for j in '0123':

for k in '0123':

if (int(i)+int(k)) > int(j):

count += 1

print(count)

k = 0

for a in range(1, 4): # a = 1, 2, 3

for b in range(0, 4): # b = 0, 1, 2, 3

for c in range(0, 4): # c = 0, 1, 2, 3

if (a + c) > b:

k += 1

print('a=',a,'b=',b,'c=',c,'k=',k)

from itertools import product

alphabet = '0123456'

ap=[]

for i in product(alphabet, repeat=4):

if i[0] > i[1] > i[2] > i[3]:

ap.append(i)

print(len(ap))

k = 0

for i1 in range(7):

for i2 in range(7):

for i3 in range(7):

for i4 in range(7):

if i1 > i2 and i2 > i3 and i3 > i4:

k += 1

print(k)

def f7(x):

s = ''

while x:

s = str(x%7) + s

x = x//7

return s

k = 0

for i in range(int('6666',7)+1):

s = f7(i)

if len(s) == 4 and s[0] > s[1] > s[2] > s[3] :

k+=1

print(k)

from itertools import product

count = 0

for p in product("ПЯТ­НИ­ЦА", repeat=5):

if p.count("Я") == 1 and p[0]!="Н":

count+=1

print(count)

a = {0: "П", 1: "Я", 2: "Т", 3: "Н", 4: "И", 5: "Ц", 6: "А"}

count = 0

for i in range(0, len(a)):

for j in range(0, len(a)):

for g in range(0, len(a)):

for m in range(0, len(a)):

for n in range(0, len(a)):

s = a[i] + a[j] + a[g] + a[m] + a[n]

if a[i] != 'Н' and s.count('Я') == 1:

count += 1

print(count)

import itertools

alphabet = "01234567"

cet = "0246"

necet = "1357"

ar = itertools.permutations(alphabet, 5)

arl = []

for e in ar:

arl.append(list(e))

count = 0

for e in arl:

flag = True

for i in range(len(e)-1):

if (e[i] in cet and e[i+1] in cet) or (e[i] in necet and e[i+1] in necet) or e[0] == '0' or e.count('1') != 0:

flag = False

if flag:

count += 1

print(count)

from itertools import *

word = '0234567'

count = 0

for i in permutations(word,5):

x = ''.join(i)

if x[0] != '0':

x = x.replace('7','1').replace('5','1').replace('3','1').replace('6','0').replace('4','0').replace('2','0')

if ('00' not in x) and ('11' not in x):

count += 1

print(count)

from itertools import*

s = permutations('01234567',5)

cnt = 0

for i in s:

p=''.join(i)

if p[0]!='0' and p.count('1')==0:

if int(p[0])%2 != int(p[1])%2 and int(p[1])%2 != int(p[2])%2 and int(p[2])%2 != int(p[3])%2 and int(p[3])%2 != int(p[4])%2:

cnt += 1

print(cnt)

cnt = 0

for i in range(1, 100000):

i = str(oct(i)[2:])

if len(i) == 5 and '1' not in i:

p = [int(d) for d in i]

if len(set(p)) == 5:

if all(p[i]%2 != p[i+1]%2 for i in range(4)):

cnt += 1

print(cnt)

import itertools

alphabet = "0123456789"

cet = "02468"

necet = "13579"

ar = itertools.permutations(alphabet, 4) #Раз­ме­ще­ние

arl = []

for e in ar:

arl.append(e)

count = 0

for e in arl:

flag = True

for i in range(len(e)-1):

if (e[i] in cet and e[i+1] in cet) or (e[i] in necet and e[i+1] in necet) or e[0] == '0':

flag = False

if flag:

count += 1

print(count)

k=0

for x in range(1000,10000):

s=str(x)

sp={s[0],s[1],s[2],s[3]}

a1='13579'

a0='02468'

fl=True

for x in range(3):

if s[x] in a1 and s[x+1] in a1 or s[x] in a0 and s[x+1] in a0:

fl=False

if len(sp)==4 and fl==True: k+=1

print(k)

from itertools import permutations

count = 0

for s in permutations('0123456789', 4):

num = ''.join(s)

if num[0] != '0':

num = num.replace('0', '2').replace('4', '2').replace('6', '2').replace('8', '2')

num = num.replace('3', '1').replace('5', '1').replace('7', '1').replace('9', '1')

if '11' not in num and '22' not in num:

count += 1

print(count)

from itertools import permutations

def good(p):

return p[0] != '0' and all([int(p[i])%2!=int(p[i+1])%2 for i in range(len(p)-1)])

print(len([p for p in permutations('0123456789',4) if good(p)]))

from itertools import *

x = permutations('0123456789', 4)

count = 0

for i in x:

if (int(i[0]) % 2 != int(i[1]) % 2) and (int(i[1]) % 2 != int(i[2]) % 2) and (int(i[2]) % 2 != int(i[3]) % 2) and i[0] != '0':

count += 1

print(count)

k = 0

for a in '2468':

for b in '13579':

for c in '02468':

for d in '13579':

s = a+b+c+d

if a != c and b != d:

k += 1

for a in '13579':

for b in '02468':

for c in '13579':

for d in '02468':

s = a+b+c+d

if a != c and b != d:

k += 1

print(k)

print(sum(1 for n in range(1000,10000) if len(set(s:=str(n)))==4 and all(int(s[i])%2 != int(s[i+1])%2 for i in range(3))))

from itertools import product

count = 0

for p in product("МАН­ГУСТ", repeat=6):

if p.count("М") == 2 and p[0]!="А" and p.count("У") >=1:

count+=1

print(count)

a = {0: "М", 1: "А", 2: "Н", 3: "Г", 4: "У", 5: "С", 6: "Т"}

count = 0

for i in range(0, len(a)):

for j in range(0, len(a)):

for g in range(0, len(a)):

for m in range(0, len(a)):

for n in range(0, len(a)):

for t in range(0, len(a)):

s = a[i] + a[j] + a[g] + a[m] + a[n] + a[t]

if a[i] != 'А' and s.count('М') == 2 and s.count('У') >=1:

count += 1

print(count)

from itertools import product

count = 0

number = 0

for p in product(sorted("АЛ­ГО­РИТМ"), repeat=5):

number += 1

if number % 2 != 0 and p[0]!="Г" and p.count("И") >= 2:

count+=1

print(count)

k = 0

for i in range(0,32768):

if i % 2 == 0:

octstr=oct(i)[2:].zfill(5)

c = octstr.count('2')

if c > 1 and octstr[0] != '1':

k += 1

print(k)

count = 0

for i1 in 'АЛО­РИТМ':

for i2 in 'АЛ­ГО­РИТМ':

for i3 in 'АЛ­ГО­РИТМ':

for i4 in 'АЛ­ГО­РИТМ':

for i5 in 'АЛ­ГО­РИТМ':

s = i1 + i2 + i3 + i4 + i5

if s[4] in 'АИМР' and s.count('И') >= 2:

count += 1

print(count)

from itertools import product

a=sorted([''.join(p) for p in product('АЛ­ГО­РИТМ',repeat=5)])

print(len([a[i] for i in range(len(a)) if i%2==0 and a[i][0]!='Г' and a[i].count('И')>=2]))

nol=[1]

pat=[1,8]

for i in range(1,10):

nol.append(nol[i-1]*(10-i))

for i in range(2,10):

pat.append(pat[i-1]*(10-i))

print(sum(pat)+sum(nol))

from itertools import permutations

word = '0123456789'

c = 0

for j in range(1,11):

for i in permutations(word,j):

x = ''.join(i)

if x[0] != '0' and (x[-1] == '5' or x[-1] == '0'):

c += 1

print(c + 1) #+1 слу­чай когда число равно 0

from math import perm # число раз­ме­ще­ний

print(2*sum(perm(9,k) for k in range(10)) - sum(perm(8,k) for k in range(9)))

from itertools import product

count = 0

for p in product("КОН­ФЕ­ТА", repeat=5):

if p.count("Е") == 2 and p[1]!="Ф":

count+=1

print(count)

a = {0: "К", 1: "О", 2: "Н", 3: "Ф", 4: "Е", 5: "Т", 6: "А"}

count = 0

for i in range(0, len(a)):

for j in range(0, len(a)):

for g in range(0, len(a)):

for m in range(0, len(a)):

for n in range(0, len(a)):

s = a[i] + a[j] + a[g] + a[m] + a[n]

if a[j] != 'Ф' and s.count('Е') == 2:

count += 1

print(count)

from itertools import product

print(len([p for p in product('КОН­ФЕ­ТА',repeat = 5) if p.count('Е') == 2 and p[1] != 'Ф']))

from itertools import product

count = 0

for p in product("012345678", repeat=5):

if p.count("5") == 1 and p[0]!="0":

i = p.index('5')

if i != 0 and i != 4:

if p[i - 1] not in '137' and p[i + 1] not in '137':

count+=1

elif i == 0:

if p[1] not in '137':

count+=1

elif i == 4:

if p[3] not in '137':

count += 1

print(count)

from itertools import *

count = 0

t = ['51','53', '57', '15', '35', '75']

for i in product('012345678', repeat=5):

p = ''.join(i)

if p[0] != '0' and p.count('5') == 1 and all (not i in p for i in t):

count += 1

print(count)

from itertools import product

d8='012345678'

zapret = [c+'5' for c in d8 if int(c)%2==1] + ['5'+c for c in d8 if int(c)%2==1]

a=[''.join(p) for p in product(d8,repeat=5) if p[0]!='0' and p.count('5')==1]

print(len([x for x in a if all([not z in x for z in zapret])]))

from itertools import *

c=0

p=product('012345678', repeat=5)

for i in p:

s=''.join(i)

if s[0]!='0' and s.count('3')==2:

for j in s:

if j in '1357': s=s.replace(j,'*')

if '2*' not in s and '*2' not in s:

c+=1

print(c)

from itertools import *

count = 0

w = ['12', '32', '52', '72', '21', '23', '25', '27']

for i in product('012345678', repeat=5):

s = ''.join(i)

if s[0] != '0' and s.count('3') == 2 and all (not i in s for i in w):

count += 1

print(count)

s = '012345678'

count = 0

for a in s:

for b in s:

for c in s:

for d in s:

for e in s:

temp = a + b + c + d + e

if temp[0] != '0' or a != '0':

if temp.count('3') == 2:

if all(x not in temp for x in '12 21 23 32 52 25 72 27'.split()):

count += 1

print(count)

def f(n):

s = str(n)

if len(s) == 12:

return 1

podr = []

for i in range(9):

if (int(s[-1]) + i)%2 == 0 and i > int(s[-1]):

podr.append(int(s+str(i)))

if (int(s[-1]) + i)%2 != 0 and i < int(s[-1]):

podr.append(int(s + str(i)))

return sum(f(i) for i in podr)

print(sum(f(i) for i in range(1,9)))

dp = [int(0 < d < 9) for d in range(9)]

for _ in range(11):

dp = [sum(dp[d] * (n > d if (d+n) % 2 == 0 else n < d) for d in range(9)) for n in range(9)]

print(sum(dp))

import functools

@functools.lru_cache(1000)

def kp(d,l):

if l==2: return len(dic[d])

return sum(kp(x,l-1) for x in dic[d])

dic={d:[x for x in range(9) if ((d+x)%2==0 and x > d) or ((d+x)%2==1 and x < d)] for d in range(9)}

print(sum(kp(x,12) for x in range(1,9)))

import math

print(math.comb(7,2)*(14**6-5**6-6*9*5**5))

from itertools import product

count = 0

for i in product ('01a', repeat = 8 ):

s = ''.join(i)

if s[0] != '0' and s.count('0') == 2 and s.count('a') <5:

count += 9**s.count('1') * 5**s.count('a')

print(count)

from itertools import product

s = product('123456789ABCDE', repeat=6)

count = 0

for i in s:

p = ''.join(i)

if p.count('A') + p.count('B') + p.count('C') + p.count('D') + p.count('E') < 5:

count += 1

print(count * 21) # 21 спо­соб вы­брать две по­зи­ции для нулей среди 7 цифр (пер­вым ноль быть не может).

print(int('534210',26)+1+sum(26**p for p in range(1,6)))

from itertools import product

count = 1

alf = sorted('QWERTYUIOPASDFGHJKLZXCVBNM')

for n in range(1,7):

for i in product(alf,repeat = n):

if "".join(i)=="FDECBA":

print(count)

break

count += 1

from itertools import product as p

k = 0

for n in p('0123456', repeat=5):

x0, xn = n[0], n[-1]

if x0 != '0' and not int(x0)%2 and xn not in '23' and\

n.count('1') >= 2:

k += 1

print(k)

from math import comb

ans=sum(comb(4,n-1)*5**(5-n) for n in range(2,6))+sum(4*comb(4,n)*5**(4-n) for n in range(2,5))

print(ans)

from itertools import product as p

k = 0

for n in p('012345', repeat=5):

if n[0] != '0' and n.count('5') >= 2 and n.count('1') + n.count('3')<= 3:

k += 1

print(k)

from itertools import product

print(len([x for x in product('012345',repeat=5) if x[0]!='0' and x.count('5')>=2]))

import itertools

otv = []

for i in range(2,12):

combs = [''.join(pair) for pair in itertools.combinations('123456789AB', i)]

otv.append(len(combs))

print(sum(otv))

import itertools

otv = []

for i in range(2,14):

combs = [''.join(pair) for pair in itertools.combinations('123456789ABC', i)]

otv.append(len(combs))

print(sum(otv))

def quantity(previous, length):

return 12-previous if length==1 else sum(quantity(i,length-1) for i in range(previous+1,13))

print(sum(quantity(0,length) for length in range(2,13)))

from itertools import product

count = 0

for i in product('0123456789', repeat=4):

if len(set(i)) == 4 and i[0] != '0':

if all(int(a) % 2 != int(b) % 2 for a, b in zip(i, i[1:])):

count += 1

print(count)

from itertools import *

count = 0

for x in product('0123456789', repeat =4):

if len(set(x))==4 and x[0]!='0':

x = ''.join(x)

x=x.replace('0', '*').replace('2', '*').replace('4', '*').replace('6', '*').replace('8', '*')

x=x.replace('1', '+').replace('3', '+').replace('5', '+').replace('7', '+').replace('9', '+')

if ('++' not in x) and ('**' not in x):

count += 1

print(count)

from itertools import *

count = 0

for i in permutations('0123456789', r = 4):

s = ''.join(i)

if s[0]!="0":

s = s.replace('0','*').replace('2','*').replace('4','*').replace('6','*').replace('8','*')

s = s.replace('1','!').replace('3','!').replace('5','!').replace('7','!').replace('9','!')

if ('**' not in s) and ('!!' not in s):

count += 1

print(count)

from itertools import permutations

s=permutations('0123456789', 4)

k=0

for i in s:

p=''.join(i)

if p[0]!='0':

if int(p[0])%2!=int(p[1])%2 and int(p[1])%2!=int(p[2])%2 and int(p[2])%2!=int(p[3])%2:

k+=1

print(k)

count = 0

for a in '2468':

for b in '13579':

for c in '02468':

for d in '13579':

if a!=c and b!=d:

count+=1

for a in '13579':

for b in '02468':

for c in '13579':

for d in '02468':

if a!=c and b!=d:

count+=1

print(count)

patterns = [('2468','13579','02468','13579'), ('13579','02468','13579','02468')]

print(sum(1 for p in patterns for a in p[0] for b in p[1] for c in p[2] for d in p[3] if a!=c and b!=d))

def good(s):

return len(set(s))==4 and sum([(s[i] in '13579') != (s[i+1] in '13579') for i in range(3)])==3

print(len([n for n in range(1000,10000) if good(str(n))]))

from itertools import product

count = 0

for i in product('0123456789abcde', repeat=4):

if i[0] != '0':

if i[0] != i[1] and i[1] != i[2] and i[2] != i[3]:

if i.count('8') == 1:

count += 1

print(count)

from itertools import product

count = 0

for i in product('0123456789abcdef', repeat=4):

if i[0] != '0':

if i[0] != i[1] and i[1] != i[2] and i[2] != i[3]:

if i.count('3') == 1:

count += 1

print(count)

from itertools import product

count = 0

for i in product("0123456789ABCxxx", repeat = 6):

s = ''.join(i)

if s.count("5") >= 1 and s[0] != "0":

if s.count("x") == 2 and "xx" in s:

count += 1

print(count)

from itertools import product

count = 0

for i in product("0123456789Axxx", repeat = 6):

s = ''.join(i)

if s.count("4") >= 1 and s[0] != "0":

if s.count("x") == 2 and "xx" in s:

count += 1

print(count)